universal mechanism for the intermittent route to strange nonchaotic attractors in quasiperiodically forced systems to examine the universality for the intermittent route to strange nonchaotic attractors snas we investigate the quasiperiodically forced henon map ring map and toda oscillator which are high dimensional invertible systems in these invertible systems dynamical transition to an intermittent sna occurs via a phase dependent saddle node bifurcation when a smooth torus collides with a ring shaped unstable set we note that this bifurcation mechanism for the appearance of intermittent snas is the same as that found in a simple system of the quasiperiodically forced noninvertible logistic map hence the intermittent route to snas seems to be universal in the sense that it occurs through the same mechanism in typical quasiperiodically forced systems of different nature

applications of the complex interpolation method to a von neumann algebra non commutative lp spaces non commutative lp spaces 1 p associated with a von neumann algebra are considered the paper consists of two parts in part i by making use of the complex interpolation method non commutative lp spaces are defined as interpolation spaces between the von neumann algebra in question and its predual also all expected properties such as duality and uniform convexity are proved in the frame of interpolaton theory and relative modular theory in part ii these lp spaces are compared with haagerup s lp spaces based on this comparison a non commutative analogue of the classical stein weiss interpolation theorem is obtained

strange nonchaotic attractors with wada basins a b s t r a c t we demonstrate strange nonchaotic attractors with wada basins snaswb and verify the abundance of snaswb in a quasiperiodically forced holmes map we identify the routes to the creation of the snaswb in a two parameter space the snaswb are characterized by the maximal lyapunov exponent by the estimation of the phase sensitivity exponent and by the singular continuous spectra we observe that the snas basins are totally wada basins in a large range of parameters the topological structures of the snas wada basins are distinguished by the basin cell method we investigate the underlying mechanism for the abundance of snaswb which is responsible for different types of basin cell in the absence of forcing this suggests that the snas cannot be predicted reliably for specific initial conditions these snaswb can thus be expected to occur more commonly in dynamical systems

on the continuity of the map ϑ ϑ from the predual of a w algebra abstract let be elements in the predual of a w algebra for their absolute value parts the estimate 2 1 2 is obtained

non commutative martingale transforms abstract we prove that non commutative martingale transforms are of weak type 1 1 more precisely there is an absolute constant c such that if m is a semi finite von neumann algebra and m n n 1 is an increasing filtration of von neumann subalgebras of m then for any non commutative martingale x x n n 1 in l 1 m adapted to m n n 1 and any sequence of signs e n n 1 e 1 x 1 n 2 n e n x n x n 1 1 c x n 1 for every n 2 this generalizes a result of burkholder from classical martingale theory to non commutative setting and answers positively a question of pisier and xu as applications we get the optimal order of the unconditional martingale differences umd constants of the schatten class s p when p similarly we prove that the umd constant of the finite dimensional schatten class s n 1 is of order log n 1 we also discuss the pisier xu non commutative burkholder gundy inequalities

integral mappings and the principle of local reflexivity for noncommutative l 1 spaces the operator space analogue of the strong form of the principle of local re exivity is shown to hold for any von neumann algebra predual and thus for any c algebraic dual this is in striking contrast to the situation for c algebras since for example k h does not have that property the proof uses the kaplansky density theorem together with a careful analysis of two notions of integrality for mappings of operator spaces

the positive contractive part of a noncommutative lp space is a complete jordan invariant abstract let 1 p we show that the positive part of the closed unit ball of a non commutative l p space as a metric space is a complete jordan invariant for the underlying von neumann algebra

complexity in hamiltonian driven dissipative chaotic dynamical systems the existence of symmetry in chaotic dynamical systems often leads to one or several low dimensional invariant subspaces in the phase space we demonstrate that complex behaviors can arise when the dynamics in the invariant subspace is hamiltonian but the full system is dissipative in particular an infinite number of distinct attractors can coexist these attractors can be quasiperiodic strange nonchaotic and chaotic with different positive lyapunov exponents finite perturbations in initial conditions or parameters can lead to a change from nonchaotic attractors to chaotic attractors however arbitrarily small perturbations can lead to dynamically distinct chaotic attractors this work demonstrates that the interplay between conservative and dissipative dynamics can give rise to rich complexity even in physical systems with a few degrees of freedom

quasiperiodically driven maps in the low dissipation limit received 24 september 2012 revised manuscript received 18 february 2013 published 11 march 2013 we study the quasiperiodically driven henon and standard maps in the weak dissipative limit in the absence of forcing there are a large number of coexisting periodic attractors although chaotic attractors can also be found these typically have vanishingly small basins of attraction quasiperiodic forcing reduces the multistability in thesystem and as the bifurcation parameter is varied strange nonchaotic attractors snas are created the attractorbasin for snas appears to be the largest among those of all coexisting attractors at such a transition doi 10 1103 physreve 87 034901 pacs number s 05

a transference method in quantum probability abstract working with a rather general notion of independence we provide a transference method which allows to compare the p norm of sums of independent copies with the p norm of sums of free copies our main technique is to construct explicit operator space l p embeddings preserving independence to reduce the problem to l 1 where some recent results by the first named author can be used we find applications on noncommutative khintchine rosenthal type inequalities and on noncommutative l p embedding theory

on an isomorphic banach mazur rotation problem and maximal norms in banach spaces abstract we prove that the spaces l p 1 p p 2 and all infinite dimensional subspaces of their quotient spaces do not admit equivalent almost transitive renormings this is a step towards the solution of the banach mazur rotation problem which asks whether a separable banach space with a transitive norm has to be isometric or isomorphic to a hilbert space we obtain this as a consequence of a new property of almost transitive spaces with a schauder basis namely we prove that in such spaces the unit vector basis of l 2 2 belongs to the two dimensional asymptotic structure and we obtain some information about the asymptotic structure in higher dimensions further we prove that the spaces l p 1 p p 2 have continuum different renormings with 1 unconditional bases each with a different maximal isometry group and that every symmetric space other than l 2 has at least a countable number of such renormings on the other hand we show that the spaces l p 1 p p 2 have continuum different renormings each with an isometry group which is not contained in any maximal bounded subgroup of the group of isomorphisms of l p

coexisting attractors in periodically modulated logistic maps we consider the logistic map wherein the nonlinearity parameter is periodically modulated for low periods there is multistability namely two or more distinct dynamical attractors coexist the case of period 2 is treated in detail and it is shown how an extension of the kneading theory for one dimensional maps can be applied in order to analyze the origin of bistability and to demarcate the principal regions of bistability in the phase space when the period of the modulation is increased char22 and here we choose periods which are the fibonacci numbers char22 the measure of multistable regions decreases the limit of quasiperiodic driving is approached in two different ways by increasing the period and keeping the drive dichotomous or by increasing the period and varying the modulation sinusoidally in the former case we find that multistability persists in small regions of the phase space while in the latter there is no evidence of multistability but strange nonchaotic attractors are created

second order global consensus in multiagent networks with random directional link failure in this paper we consider the second order globally nonlinear consensus in a multiagent network with general directed topology and random interconnection failure by characterizing the behavior of stochastic dynamical system with the corresponding time averaged system a criterion for the second order consensus is derived by constructing a lyapunov function for the time averaged network by associating the solution of random switching nonlinear system with the constructed lyapunov function a sufficient condition for second order globally nonlinear consensus in a multiagent network with random directed interconnections is also established it is required that the second order consensus can be achieved in the time averaged network and the lyapunov function decreases along the solution of the random switching nonlinear system at an infinite subsequence of the switching moments a numerical example is presented to justify the correctness of the theoretical results

synchronization and desynchronization under the influence of quasiperiodic forcing we study the influence of quasiperiodic forcing on synchronization and desynchronization using two coupled quasiperiodically forced logistic maps as a paradigm we show that due to the forcing the synchronization region in parameter space shrinks the loss of transverse stability of the synchronized attractors leads to desynchronization two types of such blowout bifurcations are described namely the blowout bifurcations of synchronized quasiperiodic motion on invariant curves and synchronized strange nonchaotic attractors both yielding desynchronized chaotic attractors

basin bifurcations in quasiperiodically forced coupled systems we study the effect of quasiperiodic forcing on a system of coupled identical logistic maps upon a variation of system parameters a variety of different dynamical regimes can be observed including phenomena such as bistability and multistability at the bifurcation to bistability in a manner reminiscent of attractor expansion at interior crises there is an abrupt change in the size of attractor basins in the bistable region attractor basins undergo additional bifurcations wherein holes and islands are created within the basins when system parameters change these can be understood by examining critical surfaces for the coupled system

ultraproducts of von neumann algebras abstract we study several notions of ultraproducts of von neumann algebras from a unified viewpoint in particular we show that for a sigma finite von neumann algebra m the ultraproduct m introduced by ocneanu is a corner of the ultraproduct m introduced by groh and raynaud using this connection we show that the ultraproduct action of the modular automorphism group of a normal faithful state of m on the ocneanu ultraproduct is the modular automorphism group of the ultrapower state t t applying these results we obtain several properties of the ocneanu ultraproduct of type iii factors which are not present in the tracial ultraproducts for instance it turns out that the ultrapower m of a type iii0 factor is never a factor moreover we settle in the affirmative a recent problem by ueda about the connection between the relative commutant of m in m and connes asymptotic centralizer algebra m

bubbling route to strange nonchaotic attractor in a nonlinear series lcr circuit with a nonsinusoidal force we identify an unconventional route to the creation of a strange nonchaotic attractor sna in a quasiperiodically forced electronic circuit with a nonsinusoidal square wave force as one of the quasiperiodic forces through numerical and experimental studies we find that bubbles appear in the strands of the quasiperiodic attractor due to the instability induced by the additional square wave type force the bubbles then enlarge and get increasingly wrinkled as a function of the control parameter finally the bubbles get extremely wrinkled while the remaining parts of the strands of the torus remain largely unaffected resulting in the creation of the sna we term this the bubbling route to the sna we characterize and confirm this creation from both experimental and numerical data using maximal lyapunov exponents and their variance poincar e maps fourier amplitude spectra and spectral distribution functions we also strongly confirm the creation of a sna via the bubbling route by the distribution of the finite time lyapunov exponents

almost completely isometric embeddings between preduals of von neumann algebras abstract we will prove that if the predual of an injective von neumann algebra is embedded in the predual of another von neumann algebra almost completely isometrically then it is complemented almost completely contractively this result is the operator space analogue of dor s theorem

dynamic triggering mechanisms for event triggered control in this technical note we present a new class of event triggering mechanisms for event triggered control systems this class is characterized by the introduction of an internal dynamic variable which motivates the proposed name of dynamic event triggering mechanism the stability of the resulting closed loop system is proved and the influence of design parameters on the decay rate of the lyapunov function is discussed for linear systems we establish a lower bound on the inter execution time as a function of the parameters the influence of these parameters on a quadratic integral performance index is also studied some simulation results are provided for illustration of the theoretical claims

harper equation the dissipative standard map and strange nonchaotic attractors relationship between an eigenvalue problem and iterated maps the almost periodic eigenvalue problem described by the harper equation is connected to other classes of quasiperiodic behavior the dissipative dynamics on critical invariant tori and quasiperiodically driven maps firstly the strong coupling limit of the supercritical harper equation and the strong dissipation limit of the critical standard map play equivalent role in describing the universal characteristics of these systems secondly a simple transformation is used to relate the harper equation to a quasiperiodically forced one dimensional map in this case the localized eigenstates of the supercritical harper equation correspond to strange but nonchaotic attractors of the driven map furthermore the existence of localization in the eigenvalue problem is associated with the appearance of homoclinic points in the corresponding map

route to chaos via strange non chaotic attractors the route to chaos in quasiperiodically forced systems is investigated it has been found that chaotic behaviour is obtained after the breaking of three frequency torus but strange non chaotic attractors are present before three frequency quasiperiodic behaviour occurs

noncommutative lp structure encodes exactly jordan structure abstract we prove that for all 1 p p 2 the l p spaces associated to two von neumann algebras m n are isometrically isomorphic if and only if m and n are jordan isomorphic this follows from a noncommutative l p banach stone theorem a specific decomposition for surjective isometries of noncommutative l p spaces

period adding bifurcation in a logistic map with memory we introduce a single step memory dependence in the fully chaotic logistic map this makes it a two dimensional system in general however we show that by using composite functions to define two one dimensional maps it is possible to obtain some analytic results for the bifurcation structure numerical results support the calculated bifurcation scheme and in addition yield a further insight which allows the calculation of the convergence ratio for a new period adding scenario

the birth of strange nonchaotic attractors abstract a mechanism is described for the development of strange nonchaotic attractors from two frequency quasiperiodic attractors in quasiperiodically driven maps this mechanism is intimately tied to the phenomenon of torus doubling the transition to strange nonchaotic behavior occurs when a period doubled torus collides with its unstable parent torus as the collision is approached the period doubled torus becomes extremely wrinkled ultimately becoming fractal at the collision the lyapunov exponent remains negative through the collision these collisions are shown to be a new type of attractor merging crisis the new feature is the possibility of nonchaotic attractors taking part in the crisis this mechanism is illustrated via numerical and analytical studies of a quasiperiodically driven logistic map

reduction of the synchronization time in random logistic maps we report on the effects of additive noises in a nonchaotic logistic map in this system the lyapunov exponent changes from negative to positive as the noise intensity is increased when the lyapunov exponent is negative the synchronization of orbits with different initial conditions occurs we find that the synchronization time cannot be determined solely by the lyapunov exponent when the noise intensity is greater than a point at which the lyapunov exponent is minimum we show that this reduction of the synchronization time is attributed to initial nonstationary behaviors where the critical point of the logistic map plays an important role

on ℒ structures of nuclear c algebras we study the local operator space structure of nuclear c algebras it is shown that a c algebra is nuclear if and only if it is an space for some and actually for every 6 the constant provides an interesting invariant for nuclear c algebras indeed if is a nuclear c algebra then we have 1 6 and if is a unital nuclear c algebra with we show that must be stably finite we also investigate the connection between the rigid 1 structure and the rigid complete order 1 structure on c algebras where the latter structure has been studied by blackadar and kirchberg in their characterization of strong nf c algebras another main result of this paper is to show that these two local structrues are actually equivalent on unital nuclear c algebras we obtain this by showing that if a unital nuclear c algebra is a rigid 1 space then it is inner quasi diagonal and thus is a strong nf algebra it is also shown that if a unital nuclear c algebra is an 1 space then it is quasi diagonal and thus is an nf algebra

leader following consensus of multi agent systems under fixed and switching topologies the leader following consensus problem of higher order multi agent systems is considered in the system the dynamics of each agent and the leader is a linear system the control of each agent using local information is designed and detailed analysis of the leader following consensus is presented for both fixed and switching interaction topologies which describe the information exchange between the multi agent systems the design technique is based on algebraic graph theory riccati inequality and lyapunov inequality simulations indicate the capabilities of the algorithms

on subspaces of non commutative lp spaces abstract we study some structural aspects of the subspaces of the non commutative haagerup l p spaces associated with a general non necessarily semi finite von neumann algebra if a subspace x of l p contains uniformly the spaces l p n n 1 it contains an almost isometric almost 1 complemented copy of l p if x contains uniformly the finite dimensional schatten classes s p n it contains their l p direct sum too we obtain a version of the classical kadec pelczynski dichotomy theorem for l p spaces p 2 we also give operator space versions of these results the proofs are based on previous structural results on the ultrapowers of l p together with a careful analysis of the elements of an ultrapower l p u which are disjoint from the subspace l p these techniques permit to recover a recent result of n randrianantoanina concerning a subsequence splitting lemma for the general non commutative l p spaces various notions of p equiintegrability are studied one of which is equivalent to randrianantoanina s one and some results obtained by haagerup rosenthal and sukochev for l p spaces based on finite von neumann algebras concerning subspaces of l p containing l p are extended to the general case

automatic continuity of orthogonality preservers on a non commutative lp τ space abstract elements a and b of a non commutative l p space associated to a von neumann algebra n equipped with a normal semifinite faithful trace are called orthogonal if l a l b r a r b 0 where l x and r x denote the left and right support projections of x a linear map t from l p n to a normed space y is said to be orthogonality to p orthogonality preserving if t a t b p a p b p whenever a and b are orthogonal in this paper we prove that an orthogonality to p orthogonality preserving linear bijection from l p n 1 p p 2 to a banach space x is automatically continuous whenever n is a separably acting von neumann algebra if n is a semifinite factor not of type i 2 we establish that every orthogonality to p orthogonality preserving linear mapping t l p n x is continuous and invertible whenever t 0 furthermore there exists a positive constant c p 1 p p 2 so that t t 1 c p 2 for every non zero orthogonality to p orthogonality preserving linear mapping t l p n x for p 1 this inequality holds with c p 1 that is t is a multiple of an isometry

strange non chaotic attractor in a quasiperiodically forced circle map abstract we show that in the quasiperiodically forced circle map strange non chaotic attractors can appear for non linearities far from the border of chaos the destruction of a two frequency quasiperiodic torus connected with the appearance of a strange non chaotic attractor is described in detail this strange non chaotic attractor is characterized by logarithmically slow diffusion of the phase it is shown that in this regime the high order phase locking states disappear and the rotation number varies rather smoothly with the parameters

event triggering sampling based leader following consensus in second order multi agent systems in this note the problem of second order leader following consensus by a novel distributed event triggered sampling scheme in which agents exchange information via a limited communication medium is studied event based distributed sampling rules are designed where each agent decides when to measure its own state value and requests its neighbor agents broadcast their state values across the network when a locally computed measurement error exceeds a state dependent threshold for the case of fixed topology a necessary and sufficient condition is established for the case of switching topology a sufficient condition is obtained under the assumption that the time varying directed graph is uniformly jointly connected it is shown that the inter event intervals are lower bounded by a strictly positive constant which excludes the zeno behavior before the consensus is achieved numerical simulation examples are provided to demonstrate the correctness of theoretical results

quasiperiodically forced dynamical systems with strange nonchaotic attractors abstract we discuss the existence and properties of strange nonchaotic attractors of quasiperiodically forced nonlinear dynamical systems we do this by examining a particular model differential equation cos e cos 2 t where is a two frequency quasiperiodic function of t when 0 the analysis of the equation is facilitated since then it can be related to the schrodinger equation with quasiperiodic potential we show that the equation does indeed exhibit strange nonchaotic attractors and we consider the important question of whether these attractors are typical in the sense that they exist on a set of positive lebesgue measure in parameter space the equation also exhibits two and three frequency quasiperiodic behavior we also show that the strange nonchaotic attractors have distinctive frequency spectrum this property might make them experimentally observable

second dual projection characterizations of three classes of l0 closed convex bounded sets in l1 non commutative generalizations abstract we provide characterizations of convex compact for the topology of local convergence in measure subsets of non commutative l 1 spaces previously considered for classical l 1 spaces more precisely if m is a semifinite and finite von neumann algebra equipped with a distinguished semifinite faithful normal trace p m l 1 m is the non commutative yosida hewitt projection and c is a norm bounded subset of l 1 m that is convex and closed for the topology of local convergence in measure then we isolate the precise conditions on c for which p c w c is compactness preserving sequentially continuous or continuous when c w is equipped with the weak topology and c with the topology of local convergence in measure

characterization of noise induced strange nonchaotic attractors received 17 january 2006 revised manuscript received 30 march 2006 published 17 july 2006strange nonchaotic attractors snas were previously thought to arise exclusively in quasiperiodic dynami cal systems a recent study has revealed however that such attractors can be induced by noise in nonquasi periodic discrete time maps or in periodically driven ows in particular in a periodic window of such asystem where a periodic attractor coexists with a chaotic saddle nonattracting chaotic invariant set none ofthe lyapunov exponents of the asymptotic attractor is positive small random noise is incapable of causingcharacteristic changes in the lyapunov spectrum but it can make the attractor geometrically strange bydynamically connecting the original periodic attractor with the chaotic saddle here we present a detailed studyof noise induced snas and the characterization of their properties numerical calculations reveal that thefractal dimensions of noise induced snas typically assume fractional values in contrast to snas in quasip eriodically driven systems whose dimensions are integers an interesting nding is that the uctuations of the nite time lyapunov exponents away from their asymptotic values obey an exponential distribution thegenerality of which we are able to establish by a theoretical analysis using random matrices we suggest apossible experimental test we expect noise induced snas to be general doi 10 1103 physreve 74 016203 pacs number s 05 45 gg

exponential consensus of general linear multi agent systems under directed dynamic topology this paper aims to investigate the consensus control of generic linear multi agent systems mass under directed dynamic topology nonnegative matrix theory in particular the product properties of infinite row stochastic matrices which are widely used for multiple integrator agents is explored to deal with the convergence analysis of generic linear mass it is finally shown that the exponential consensus can be reached under very relaxed conditions i e the directed interaction topology is only required to be repeatedly jointly rooted and the exponentially unstable mode of each individual system is weak enough moreover a least convergence rate and a bound for the unstable mode of the individual agent system both of which are independent of the switching mode can be explicitly specified

colp spaces the local structure of non commutative lp spaces abstract developing the theory of col p spaces a variation of the non commutative analogue of l p spaces we provide new tools to investigate the local structure of non commutative l p spaces under mild assumptions on the underlying von neumann algebras non commutative l p spaces with grothendieck s approximation property behave locally like the space of matrices equipped with the p norm of the sequences of their singular values as applications we obtain a basis for non commutative l p spaces associated with hyperfinite von neumann algebras with separable predual von neumann algebras generated by free groups and obtain a basis for separable nuclear c algebras

strange attractors that are not chaotic abstract it is shown that in certain types of dynamical systems it is possible to have attractors which are strange but not chaotic here we use the word strange to refer to the geometry or shape of the attracting set while the word chaotic refers to the dynamics of orbits on the attractor in particular the exponential divergence of nearby trajectories we first give examples for which it can be demonstrated that there is a strange nonchaotic attractor these examples apply to a class of maps which model nonlinear oscillators continuous time which are externally driven at two incommensurate frequencies it is then shown that such attractore are persistent under perturbations which preserve the original system type i e there are two incommensurate external driving frequencies this suggests that for systems of the typw which we have considered nonchaotic strange attractors may be expected to occur for a finite interval of parameter values on the other hand when small perturbations which do not preserve the system type are numerically introduced the strange nonchaotic attractor is observed to be converted to a periodic or chaotic orbit thus we conjecture that in general continuous time systems flows which are not externally driven at two incommensurate frequencies should not be expected to have strange nonchaotic attractors except possibly on a set of measure zero in the parameter space

bifurcations and transitions in the quasiperiodically driven logistic map abstract we discuss several bifurcation phenomena that occur in the quasiperiodically driven logistic map this system can have strange nonchaotic attractors snas in addition to chaotic and regular attractors on snas the dynamics is aperiodic but the largest lyapunov exponent is nonpositive there are a number of different transitions that occur here from periodic attractors to snas from snas to chaotic attractors etc we describe some of these transitions by examining the behavior of the largest lyapunov exponent distributions of finite time lyapunov exponents and the invariant densities in the phase space

les espaces lp d une algebre de von neumann definies par la derivee spatiale abstract this work answers a question raised by a connes on the spatial theory of von neumann algebras preprint inst hautes etudes sci france and generalizes for a general von neumann algebra the theory of non commutative integration of j dixmier bull soc math france 81 1953 and i segal ann of math 57 1973

decentralized event triggered consensus with general linear dynamics the consensus problem with general linear dynamics and undirected graphs is studied in this paper by means of event triggered control strategies a novel consensus protocol is proposed where each agent implements a model of the decoupled dynamics of its neighbors under this control strategy transmission of information does not occur continuously but only at discrete points in time the approach presented in this paper provides both a decentralized control law and a decentralized communication policy we are able to design thresholds that only depend on local information and guarantee asymptotic consensus positive inter event times are guaranteed for particular cases of the linear dynamics in an extension a positive constant is added to the thresholds in order to exclude zeno behavior for general linear dynamics the difference between agents trajectories can be bounded in this case and bounds on the state disagreement are derived

distributed algebraic connectivity estimation for undirected graphs with upper and lower bounds the algebraic connectivity of the graph laplacian plays an essential role in various multi agent control systems in many cases a lower bound of this algebraic connectivity is necessary in order to achieve a certain performance lately several methods based on distributed power iteration have been proposed for computing the algebraic connectivity of a symmetric laplacian matrix however these methods cannot give any lower bound of the algebraic connectivity and their convergence rates are often unclear in this paper we present a distributed algorithm for estimating the algebraic connectivity for undirected graphs with symmetric laplacian matrices our method relies on the distributed computation of the powers of the adjacency matrix and its main interest is that at each iteration agents obtain both upper and lower bounds for the true algebraic connectivity both bounds successively approach the true algebraic connectivity with the convergence speed no slower than o 1 k

birth of strange nonchaotic attractors due to interior crisis abstract we study the interior crisis in the period 3 window of the quasiperiodically forced logistic map two routes from quasiperiodicity to chaos involving strange nonchaotic attractors sna are discovered along one route we observe a sudden widening of the sna this is similar to the interior crisis in chaotic systems along the other route we find a direct transition from an invariant curve to a strange nonchaotic attractor exactly at the interior crisis point this is a new mechanism of the appearance of strange nonchaotic attractors beyond the interior crisis the temporal behavior can be described as a crisis induced intermittency whose scaling behavior is discussed

noncommutative burkholder rosenthal inequalities we investigate martingale inequalities in noncommutative lp spaces associated with a von neumann algebra equipped with a faithful normal state we prove the noncommutative analogue of the classical burkholder inequality on the conditioned or little square function and extend the noncommutative burkholder gundy inequalities from comm math phys 189 1997 667 698 to this nontracial setting we include several related results

correlations and spectra of strange non chaotic attractors we consider correlations and spectra of strange nonchaotic attractors in quasiperiodically driven nonlinear systems it is demonstrated that a self similar autocorrelation function and a singular continuous spectrum may be observed in such systems the properties of correlations and spectra depend very subtly on the rotation number of the quasiperiodic force and on the parameters of the system for some parameter values the usual discrete spectrum is restored

event based agreement protocols for multi agent networks abstract this paper considers an average consensus problem for multiple integrators over fixed or switching undirected and connected network topologies event based control is used on each agent to drive the state to their initial average eventually an event triggering scheme is designed based on a quadratic lyapunov function the derivative of the lyapunov function is made negative by an appropriate choice of the event condition for each agent the event condition is sampled data and distributed in the sense that the event detector uses only neighbor information and local computation at discrete sampling instants the event based protocol design is illustrated with simulations

doubling bifurcations of destroyed t 2 tori abstract two duffing oscillators driven with incommensurate frequencies and coupled additively are investigated with this system we observe a host of complex behavior which compete with each other in parameter space in particular the period doubling of an attracting t 2 torus and the destruction of a t 2 torus as the parameters are varied along a curve in parameter space we observe period doubling bifurcations of a destroyed t 2 torus this phenomenon is studied in greater detail via a simple recursive map

measures of weak non compactness in preduals of von neumann algebras and jbw triples abstract we prove among other results that three standard measures of weak non compactness coincide in preduals of jbw triples this result is new even for preduals of von neumann algebras we further provide a characterization of jbw triples with strongly wcg predual and describe the order of seminorms defining the strong topology as a byproduct we improve a characterization of weakly compact subsets of a jbw triple predual providing so a proof for a conjecture open for almost eighteen years on weakly compact operators from a jb triple into a complex banach space

distributed estimation and control of algebraic connectivity over random graphs in this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad hoc networks in the presence of a random topology first given a generic random graph we introduce a novel stochastic power iteration method that allows each node to estimate and track the algebraic connectivity of the underlying expected graph using results from stochastic approximation theory we prove that the proposed method converges almost surely a s to the desired value of connectivity even in the presence of imperfect communication scenarios the estimation strategy is then used as a basic tool to adapt the power transmitted by each node of a wireless network in order to maximize the network connectivity in the presence of realistic medium access control mac protocols or simply to drive the connectivity toward a desired target value numerical results corroborate our theoretical findings thus illustrating the main features of the algorithm and its robustness to fluctuations of the network graph due to the presence of random link failures

fixed point properties of semigroups of nonexpansive mappings abstract we prove that if h is a hilbert space then the schatten trace class operators on h has the weak fixed point property for left reversible semigroups this answered positively a problem raised by a t m lau we also prove that if m is a finite von neumann algebra then any nonempty bounded convex subset of the non commutative l 1 space associated to m that is compact for the measure topology has the fixed point property for left reversible semigroups

event triggered control of multiagent systems for fixed and time varying network topologies a decentralized controller that uses event triggered communication scheduling is developed for the leader follower consensus problem under fixed and switching communication topologies to eliminate continuous interagent communication state estimates of neighboring agents are designed for control feedback and are updated via communication to reset growing estimate errors the communication times are based on an event triggered approach and are adapted based on the trade off between the control system performance and the desire to minimize the amount of communication an important aspect of the developed event trigger strategy is that communication is not required to determine when a state update is needed since the control strategy produces switched dynamics analysis is provided to show that zeno behavior is avoided by developing a positive constant lower bound on the minimum inter event interval a lyapunov based convergence analysis is also provided to indicate bounded convergence of the developed control methodology

canonical operator space structures on non commutative lp spaces we analyze canonical operator space structures on the non commutative lp spaces lp m constructed by interpolation a la stein weiss based on two normal semifinite faithful weights on a w algebra m we show that there is only one canonical i e arising by interpolation operator space structure on lp m when m and p are kept fixed namely for any n s f weights on m and 0 1 the spaces lp m are all completely isomorphic when they are canonically considered as operator spaces finally we also describe the norms on all matrix spaces mn lp m which determine such a canonical quantized structure

the structure of mode locked regions in quasi periodically forced circle maps using a mixture of analytic and numerical techniques we show that the mode locked regions of quasi periodically forced arnold circle maps form complicated sets in parameter space these sets are characterized by pinched off regions where the width of the mode locked region becomes very small by considering general quasi periodically forced circle maps we show that this pinching occurs in a broad class of such maps having a simple symmetry 2000 elsevier science b v all rights reserved

non commutative martingale inequalities we prove the analogue of the classical burkholder gundy inequalites for non commutative martingales as applications we give a characterization for an ito clifford integral to be an lp martingale via its integrand and then extend the ito clifford integral theory in l2 developed by barnett streater and wilde to lp for all 1 p we include an appendix on the non commutative analogue of the classical fefferman duality between h1 and bmo

nature of weak generalized synchronization in chaotically driven maps weak generalized synchrony in a drive response system occurs when the response dynamics is a unique but nondifferentiable function of the drive in a manner that is similar to the formation of strange nonchaotic attractors in quasiperiodically driven dynamical systems we consider a chaotically driven monotone map and examine the geometry of the limit set formed in the regime of weak generalized synchronization the fractal dimension of the set of zeros is studied both analytically and numerically we further examine the stable and unstable sets formed and measure the regularity of the coupling function the stability index as well as the dimension spectrum of the equilibrium measure can be computed analytically

torus doubling bifurcations and strange nonchaotic attractors in a vibro impact system whether strange nonchaotic attractors snas can occur typically in dynamical systems other than quasiperiodically driven systems has been an open problem here we show that the snas can be induced by the interruption of torus doubling bifurcation in a periodically driven vibro impact system it is found that the creation of snas occurs due to the collision of doubled torus with some unstable periodic orbits based on the poincare map technique two types of codimension 3 bifurcations are represented and typical torus doubling bifurcations can occur in the neighborhood of these bifurcation points we use the singular continuous fourier spectrum and its scaling to verify the strangeness nondifferentiability of the attractors the implicitly transcendental map is used to calculate the largest lyapunov exponent by qr based algorithm which ensures that the underlying dynamics with nonpositive lyapunov exponents is nonchaotic the associated mechanism is described for the creation of snas through detecting unstable periodic orbits from poincare map series

perturbation of ell_1 copies in preduals of jbw triples abstract it is known that two normal functionals on a jbw triple are orthogonal i e they have orthogonal support tripotents if and only if they are l orthogonal meaning that they span an isometric copy of l 1 2 this is shown to be stable under small norm perturbations in the following sense if the linear span of the two functionals is isometric up to 0 to l 1 2 then the functionals are less far in norm than e 0 from two orthogonal functionals where e 0 as 0 analogous statements for finitely and even infinitely many functionals hold as well and so does a corresponding statement for non normal functionals