limits of hypercyclic and supercyclic operators abstract an operator t on a complex separable infinite dimensional hilbert space h is hypercyclic if there is a vector y in h such that the orbit y ty t2y is dense in h it is shown that if t is hypercyclic then t does not have any eigenvalue and that the union of the spectrum of t and the unit circle is a connected set this result is used to obtain a spectral characterization of the norm closure of the class hc h of all hypercyclic operators acting on h as well as a formula for the distance from a given operator to hc h analogous results are obtained for the closely related class sc h of all supercyclic operators this paper includes some information about the structure of the set of all hypercyclic supercyclic vectors of a given hypercyclic supercyclic resp operator t

common hypercyclic vectors for multiples of backward shift we prove that l 2 contains a dense set of vectors which are hypercyclic simultaneously for all multiples of the backward shift oper ator by constants of absolute value greater than 1

chaotic polynomials on banach spaces we show the existence of chaotic in the sense of devaney polynomials on banach spaces of q summable sequences such polynomials p consist of composition of the backward shift with a certain fixed polynomial p of one complex variable on each coordinate in general we also prove that p is chaotic in the sense of auslander and yorke if and only if 0 belongs to the julia set of p

characterizations of the subdifferential of convex integral functions under qualification conditions abstract this work provides formulae for the e subdifferential of integral functions in the framework of complete finite measure spaces and locally convex spaces in this work we present here new formulae for this e subdifferential under the presence of continuity type qualification conditions relying on the data involved in the integrand

hankel convolution operators on entire functions and distributions in this paper we study the hankel convolution operators on the space of even and entire functions and on schwartz distribution spaces we characterize the hankel convolution operators as those ones that commute with hankel translations and with a bessel operator also we prove that the hankel convolution operators are hypercyclic and chaotic on the spaces under consideration

design of controllers for mg3 compressor models with general characteristics using graph backstepping we discuss the design of controllers for compressors with general characteristics including the right skewed ones the controllers can be represented graphically by plotting their throttle surfaces the graphical representation of controllers enhances understanding of controller action and allows to compare various controllers we discuss the issue of the right skewness of a compressor characteristic we show how to design controllers using a graph backstepping procedure involving the construction of the throttle surface we show that for a quite general compressor characteristic every potential axisymmetric equilibrium on the decreasing part of the compressor characteristic the peak of the characterisitic and every rotating stall equilibrium close to the peak can be globally or semi globally stabilized by an appropriate choice of the throttle surface and the controller gains we obtain lower bounds on the gains of the controller in terms of the divided differences related to compressor characteristic these bounds can be expressed using some bounds on the first and second derivatives of the characteristic in the region of operation in this way we establish a direct relationship between the shape of the compressor characteristic and the required controller gains we discuss controllers that stabilize a range of the desired equilibria and guarantee a soft bifurcation of the equilibria as a set point parameter varies we give an example of controller design for a right skew compressor we provide simple general guidelines for choosing the throttle surface

topologically transitive semigroup actions of real linear fractional transformations abstract let f i f i i f x a x b c x d a d b c 0 where i is a proper closed subinterval of r our main goal in this paper is to describe all f g f i such that the action of the semigroup generated by f and g is topologically transitive on i we also prove that this action is never weakly topologically mixing finally we describe all pairs of affine functions on r whose generated semigroup action is weakly topologically mixing

mean ergodic composition operators on banach spaces of holomorphic functions abstract given a symbol i e a holomorphic endomorphism of the unit disc we consider the composition operator c f f defined on the banach spaces of holomorphic functions a d and h d we obtain different conditions on the symbol which characterize when the composition operator is mean ergodic and uniformly mean ergodic in the corresponding spaces these conditions are related to the asymptotic behavior of the iterates of the symbol finally we deal with some particular case in the setting of weighted banach spaces of holomorphic functions

subdifferential representation formula and subdifferential criteria for the behavior of nonsmooth functions abstract several kinds of behaviors of extended real valued lower semicontinuous functions are known to be equivalent to certain appropriate conditions in terms of the clarke subdifferential the paper provides a systematic study showing that any such condition with the clarke subdifferential is valid if and only if it holds with any operator representing the clarke subdifferential like in the subdifferential proximal formula

on universal subsets of banach spaces we prove that to most of the known hypercyclic operators a on separable banach spaces there exist compact compact convex compact connected subsets k of e such that each compact compact convex compact connected subset of e can be approximated with respect to hausdorff s distance by a n k for suitable n in mathbb n

localized versions of function spaces and generic results abstract we consider generalizations of classical function spaces by requiring that a holomorphic in function satisfies some property when we approach from not the whole boundary but only a part of it these spaces endowed with their natural topology are frechet spaces we prove some generic non extendability results in such spaces and generic nowhere differentiability on the corresponding part of

hypercyclic weighted shifts an operator t acting on a hilbert space is hypercyclic if for some vector x in the space the orbit tnx n 0 is dense in this paper we characterize hypercyclic weighted shifts in terms of their weight sequences and identify the direct sums of hypercyclic weighted shifts which are also hypercyclic as a consequence we show within the class of weighted shifts that multi hypercyclic shifts and direct sums of fixed hypercyclic shifts are both hypercyclic for general hypercyclic operators the corresponding questions were posed by d a herrero and they still remain open using a different technique we prove that i t is hypercycic whenever t is a unilateral backward weighted shift thus answering in more generality a question recently posed by k c chan and j h shapiro

hypercyclic bilinear operators on banach spaces abstract we study the dynamics induced by an m linear operator we answer a question of bes and conejero showing an example of an m linear hypercyclic operator acting on a banach space moreover we prove the existence of m linear hypercyclic operators on arbitrary infinite dimensional separable banach spaces we also prove an existence result about symmetric bihypercyclic bilinear operators answering a question by grosse erdmann and kim

algebraic genericity of frequently universal harmonic functions on trees abstract we show that the set of frequently universal harmonic functions on a tree t contains a vector space except 0 which is dense in the space of harmonic functions on t seen as subset of c t in order to prove this we replace the complex plane c by any separable frechet space e and we repeat all the theory

disjointness in hypercyclicity we introduce a notion of disjointness for finitely many hypercyclic operators acting on a common space notion that is weaker than furstenberg s disjointness of fluid flows we provide a criterion to construct disjoint hypercyclic operators that generalizes some well known connections between the hypercyclicity criterion hereditary hypercyclicity and topological mixing to the setting of disjointness in hypercyclicity we provide examples of disjoint hypercyclic operators for powers of weighted shifts on a hilbert space and for differentiation operators on the space of entire functions on the complex plane

semi fredholm theory hypercyclic and supercyclic subspaces a vector x in a banach space cal b is called hypercyclic for a bounded linear operator t cal b rightarrow cal b if the orbit t n x n geq 1 is dense in cal b we prove that if t is hereditarily hypercyclic and its essential spectrum meets the closed unit disk then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t the converse is also true even if t is not hereditarily hypercyclic in this way we improve and extend to banach spaces a recent result for hilbert spaces we also investigate the corresponding problem for supercyclic operators in this case we obtain a description of the norm closure of the class of all supercyclic operators that have an infinite dimensional closed subspace of hypercyclic vectors moreover for certain kinds of supercyclic operators we can characterize when they have an infinite dimensional closed subspace of supercyclic vectors 1991 mathematics subject classification 47b38 47b99

hypercyclic operators that commute with the bergman backward shift the backward shift b on the bergman space of the unit disc is known to be hypercyclic meaning it has a dense orbit here we ask which operators that commute with b inherit its hypercyclicity we show that the problem reduces to the study of operators of the form 9p b where so is a holomorphic self map of the unit disc that multiplies the dirichlet space into itself and that the question of hypercyclicity for such an operator depends on how freely 9p z is allowed to approach the unit circle as lz s 1

bifurcation analysis of axial flow compressor stability with a one mode truncation it is possible to reduce the moore greitzer model for compressor instability to a set of three ordinary differential equations these are approached from the point of view of bifurcation theory most of the bifurcations emerge from a degenerate takens bogdanov bifurcation point the bifurcation sets are completed using the numerical branch tracking scheme auto despite the severity of the truncation the agreement with experimental results is excellent

hereditarily hypercyclic operators abstract we show that a continuous linear operator t on a frechet space satisfies the so called hypercyclicity criterion if and only if it is hereditarily hypercyclic and if and only if the direct sum t t is hypercyclic in particular hypercyclic operators with either a dense generalized kernel or a dense set of periodic points i e chaotic in the sense of r l devaney 1989 an introduction to chaotic dynamical systems addison wesley reading ma must satisfy the criterion finally we provide a characterization of those weighted shifts t that are hereditarily hyper cyclic with respect to a given sequence n k of positive integers as well as conditions under which t and t n k k 1 share the same set of hypercyclic vectors

hypercyclic and cyclic vectors abstract let x denote an arbitrary separable banach space over the field of complex numbers and b x the banach algebra of all bounded linear operators on x we prove the following results 1 an element of the space x is hypercyclic supercyclic for all positive powers tn of an operator t in b x if it is hypercyclic supercyclic for t 2 under some condition on the spectrum of the adjoint of a cyclic operator the set of all cyclic vectors of the operator is dense this result extends to any cyclic commutative subset of b x 3 under a mild condition on the spectrum of a cyclic operator t the set of all separating vectors for the commutant t of t is dense this also extends to any cyclic commutative subset of b x 4 a slightly stronger version of a theorem of k f clancey and d d rogers on cyclic vectors finally we define and discuss hereditarily hypercyclic operators

basic control for the viscous moore greitzer partial differential equation the notions of basic controllability and basic control are defined a quadratic optimal control of the linearized viscous moore greitzer equation is presented and it is confirmed that stall is uncontrollable in this model a basic control is constructed for the nonlinear viscous moore greitzer equation which can control both surge and stall some extensions of this construction are discussed numerical simulations of the basic control are presented and its performance is compared to the performance of a backstepping control constructed by banaszuk hauksson and mezic siam j control optim 37 1999 pp 1503 1537 it is shown that the viscous moore greizer equation with throttle control is not basically controllable but under certain conditions adding air injection control will make the equation basically controllable

cyclicity of bicyclic operators and completeness of translates we study cyclicity of operators on a separable banach space which admit a bicyclic vector such that the norms of its images under the iterates of the operator satisfy certain growth conditions a simple consequence of our main result is that a bicyclic unitary operator on a banach space with separable dual is cyclic our results also imply that if s a n n in mathbb z longmapsto a n 1 n in mathbb z is the shift operator acting on the weighted space of sequences ell omega 2 mathbb z if the weight satisfies some regularity conditions and n 1 for nonnegative n then s is cyclic if rm lim n rightarrow infty rm log omega n sqrt n 0 on the other hand one can see that s is not cyclic if the series sum n geq 1 rm log omega n n 2 diverges we show that the question of herrero whether either s or s is cyclic on ell omega 2 mathbb z admits a positive answer when the series sum n in mathbb z rm log s n n 2 1 is convergent we also prove completeness results for translates in certain banach spaces of functions on mathbb r

universality of holomorphic functions bounded on closed sets in this note the existence of translation universal entire functions which are bounded on certain closed subsets is characterized in terms of topological and geometrical properties of such subsets corresponding results are also stated in the space of holomorphic functions on the unit disk and in the space of harmonic functions on the plane moreover it is shown the existence of entire functions which are bounded on many rays and simultaneously are universal with respect to a prescribed infinite order differential operator

uniform approximation of bloch functions and the boundedness of the integration operator on h abstract we obtain a necessary and sufficient condition for the operator of integration to be bounded on h in a simply connected domain the main ingredient of the proof is a new result on uniform approximation of bloch functions

existence of common and upper frequently hypercyclic subspaces abstract we provide criteria for the existence of upper frequently hypercyclic subspaces and for common hypercyclic subspaces which include the following consequences there exist frequently hypercyclic operators with upper frequently hypercyclic subspaces and no frequently hypercyclic subspace on the space of entire functions each differentiation operator induced by a non constant polynomial supports an upper frequently hypercyclic subspace and the family of its non zero scalar multiples has a common hypercyclic subspace a question of costakis and sambarino on the existence of a common hypercyclic subspace for a certain uncountable family of weighted shift operators is also answered

hypercyclic tuples of operators and somewhere dense orbits in this paper we prove that there are hypercyclic n 1 tuples of diagonal matrices on cn and that there are no hypercyclic n tuples of diagonalizable matrices on cn we use the last result to show that there are no hypercyclic subnormal tuples in infinite dimensions we then show that on real hilbert spaces there are tuples with somewhere dense orbits that are not dense but we also give sufficient conditions on a tuple to insure that a somewhere dense orbit on a real or complex space must be dense

common hypercyclic functions for translation operators with large gaps abstract let h c be the set of entire functions endowed with the topology of local uniform convergence fix a sequence of non zero complex numbers n n which satisfies the following property for every m 0 there exists a subsequence n of n such that i n 1 n m for every n 1 2 and ii n 1 1 n we prove that there exists a residual set g h c such that for every f g and every non zero complex number a the set f z n a n 1 2 is dense in h c this answers in the affirmative question 1 in 29 and it also provides an extension of a theorem due to costakis and sambarino in 32

a finite dimensional attractor of the moore greitzer pde model the moore greitzer pde model with viscosity is presented and the equations are rewritten as an evolution equation on a hilbert space it is proven that the model has a unique global solution which is smooth in space and time furthermore it is proven that there exists a global attractor i e a compact set which attracts all bounded sets finally it is shown that the attractor has a finite fractal dimension

existence of hypercyclic operators on topological vector spaces the present paper introduces a very simple but very useful notion of the so called quasi extension ofl1 operators and proves that a large class of topological vector spaces admit continuous hypercyclic operators in particular it answers in the affirmative a question of s rolewicz posed in 1969 whether or not every infinite dimensional separable banach space admits a continuous hypercyclic operator

subdifferential of the closed convex hull of a function and integration with nonconvex data in general normed spaces in this paper we approach the study of the subdifferential of the closed convex hull of a function and the related integration problem without the usual assumption of epi pointedness the key tool is as in hiriart urruty et al 2011 7 the concept of e subdifferential some other assumptions which are standard in the literature are also removed

integration of fenchel subdifferentials of epi pointed functions it is shown that in finite dimensions rockafellar s technique of integrating cyclically monotone operators applied to the fenchel subdifferential of an epi pointed function yields the closed convex hull of that function

invariant gaussian measures for operators on banach spaces and linear dynamics we give conditions for an operator t on a complex separable banach space x with sufficiently many eigenvectors associated to eigenvalues of modulus 1 to admit a non degenerate invariant gaussian measure with respect to which it is weak mixing the existence of such a measure depends on the geometry of the banach space and on the possibility of parametrizing the mathbb t eigenvector fields of t in a regular way we also investigate the connection with frequent hypercyclicity

hypercyclic operators on non normable frechet spaces abstract every infinite dimensional separable non normable frechet space admits a continuous hypercyclic operator a large class of separable countable inductive limits of banach spaces with the same property is given but an example of a separable complete inductive limit of banach spaces which admits no hypercyclic operator is provided it is also proved that no compact operator on a locally convex space is hypercyclic

integration formulas via the fenchel subdifferential of nonconvex functions abstract starting from explicit expressions for the subdifferential of the conjugate function we establish in the banach space setting some integration results for the so called epi pointed functions these results use the e subdifferential and the fenchel subdifferential of an appropriate weak lower semicontinuous lsc envelope of the initial function we apply these integration results to the construction of the lsc convex envelope either in terms of the e subdifferential of the nominal function or of the subdifferential of its weak lsc envelope

generic approximation of functions by their pade approximants abstract in the present article we obtain generic approximations under sharp conditions of holomorphic functions on arbitrary open sets by sequences of their pade approximants similar results hold for functions smooth on the boundary of their domain of definition in addition the approximation is valid simultaneously with respect to all centers of expansion

a dynamical characterization of sub arakelian subsets abstract we are going to characterize those sets which can be covered by an arakelian set in terms of dynamical properties of entire functions via similarities moreover if we consider the set of universal entire functions via similarities that are bounded on such a sub arakelian set then it is shown that its algebraic size is as large as possible as a consequence we prove that the set of universal entire functions bounded on every straight line is algebraically large

a nonlinear age and maturity structured model of population dynamics i basic theory a nonlinear model of age and maturity structured population dynamics is analyzed the population is structured by age and maturity of the individuals and the nonlinearity in the equations corresponds to density dependent limitation of population growth the existence and asymptotic behavior of solutions are studied

some remarks on abstract universal series abstract we introduce a new class of universal series in the abstract setting this class lies between two already known classes of universal series by two examples we differentiate these classes these examples are the first examples in the case where all classes are non void we also prove that the class of universal series where the approximating indexes have upper density 1 is dense and g and that the class of lower frequently universal series is of the first category

linear structure of hypercyclic vectors abstract a vector x in a banach space b is called hypercyclic for a bounded linear operator t b b if the orbit t n x n 1 is dense in b our main result states that if t is a compact perturbation of an operator of norm 1 and satisfies an appropiate extra hypothesis then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t in particular the result applies to compact perturbations of the identity we also include applications to some weighted backward shifts and compact perturbations of the identity by weighted backward shifts this last result in combination with a recent one that states that every banach space admits an operator with a hypercyclic vector proves that in all banach space there is an operator t with an infinite dimensional closed subspace consisting except for zero of hypercyclic vectors the main result also applies to the differentiation operator and the translation operator t f z f z 1 on certain hilbert spaces consisting of entire functions

optimal growth of entire functions frequently hypercyclic for the differentiation operator we solve a problem posed by bonilla and grosse erdmann 2007 7 by constructing an entire function f which is frequently hypercyclic with respect to the differentiation operator and satisfies mf r cerr 1 4 where c 0 may be chosen arbitrarily small this growth rate is sharp we also obtain optimal results for minimal growth in terms of average lp norms among other tools the proof uses the rudin shapiro polynomials and heat kernel estimates

brief paper local l2 gain of bifurcation stabilization local l 2 gain analysis of a class of stabilizing controllers for nonlinear systems with both stationary and hopf bifurcations is studied in particular a family of lyapunov functions is first constructed for the corresponding critical system and simplified sufficient conditions to compute the l 2 gain are derived by solving the hamilton jacobi bellman hjb inequalities local robust analysis for a class of bifurcation stabilizing controllers can then be conducted through computing the local l 2 gain achieved by these controllers at the critical situation the results obtained in this paper provide useful guidance for selecting a robust controller from a given class of stabilizing controllers in terms of l 2 gain as an example application to an axial flow compressor control is discussed in detail

determination of convex functions via subgradients of minimal norm we show in hilbert space setting that any two convex proper lower semicontinuous functions bounded from below for which the norm of their minimal subgradients coincide they coincide up to a constant moreover under classic boundary conditions we provide the same results when the functions are continuous and defined over an open convex domain these results show that for convex functions bounded from below the slopes provide sufficient first order information to determine the function up to a constant giving a positive answer to the conjecture posed in boulmezaoud et al siam j optim 28 3 2049 2066 2018

stabilization of minimum phase nonlinear systems by dynamic output feedback in this paper the stabilization problem of minimum phase nonlinear systems by dynamic output feedback is investigated it is shown that if the zero dynamics of an affine nonlinear system is asymptotically stable according to the kth approximation then the system is stabilizable by dynamic output feedback the proof is constructive which provides a method to design the stabilizer the result is applied to investigating the stabilization problem of the rotating stall in axial flow compressors

brief adaptive control of compressor surge instability in this paper we propose a simple high gain type adaptive control scheme for surge stabilization in a compression system we consider a typical configuration in which the plenum throttle position is the control input while the measured output is given by the total pressure at the compressor inlet we prove convergence of the control scheme using a simplified but widely accepted second order model the system does not satisfy strict minimum phase assumptions usually introduced in the high gain type adaptive control context and therefore the proof has been tailored to the specific problem we finally validate the proposed controller by means of both numerical simulation and experiments on a real plant

pade approximants density of rational functions in a ω and smoothness of the integration operator first we establish some generic universalities for pade approximants in the closure x in the space a of all rational functions with poles off the closure of the domain c is taken with respect to the finite plane c next we give sufficient conditions on so that x a some of these conditions imply that even if the boundary of a jordan domain has infinite length the integration operator on preserves h and a as well we also give an example of a jordan domain and a function f a such that its antiderivative is not bounded on finally we restate these results for volterra operators on the open unit disc d and we complete them by some generic results

computer aided analysis of imperfect bifurcation diagrams i simple bifurcation point and isola formation centre quantitative information from the theory for imperfect bifurcation by golubit sky and schaeffer singularities and groups in bifurcation theory vol i springer verlag new york 1985 can be obtained at the cost of some numerical effort the information is used to get a local approximation of the imperfect bifurcation diagrams for simple bifurcation points or isola formation centres

approximation by chaotic operators and by conjugate classes we show that every bounded linear operator on a separable infinite dimensional hilbert space h is the sum of two operators in the norm closure of the set of operators on h that are chaotic in the sense of devaney we also observe that the density of several classes of cyclic operators with respect to the strong operator topology may be derived from a result by hadwin et al proc amer math soc 76 1979 250 252

hypercyclic subspaces in omega abstract we show that any countable family of operators of the form p b where p is a non constant polynomial and b is the backward shift operator on the countably infinite product of lines has a common hypercyclic subspace

generic boundary behaviour of taylor series in hardy and bergman spaces it is known that generically taylor series of functions holomorphic in the unit disc turn out to be universal series outside of the unit disc and in particular on the unit circle due to classical and recent results on the boundary behaviour of taylor series for functions in hardy spaces and bergman spaces the situation is drastically different in this paper it is shown that in many respects these results are sharp in the sense that universality generically appears on maximal exceptional sets as a main tool it is proved that the taylor backward shift on certain bergman spaces is mixing

mixing simultaneous universal and disjoint universal backward φ shifts abstract spaces of sequences which are valued in a topological space e are considered in order to study universality properties of generalized backward shifts associated to certain selfmappings of e after providing a condition which guarantees the mixing property of backward shifts in terms of the dynamical properties of the generating selfmappings applications to universality theory within the framework of complex dynamics are furnished

operators with dense invariant cyclic vector manifolds abstract we study a class of banach space operators patterned after the weighted backward shifts on hilbert space and show that any non scalar operator in the commutant of one of these generalized backward shifts has a dense invariant linear manifold whose non zero members are cyclic vectors under appropriate extra hypotheses on the commuting operator stronger forms of cyclicity are possible the most extreme being hypercyclicity density of an orbit motivated by these results we examine the cyclic behavior of two seemingly unrelated classes of operators adjoint multiplications on hilbert spaces of holomorphic functions and differential operators on the frechet space of entire functions we show that each of these operators other than the scalar multiples of the identity possesses a dense invariant linear submanifold each of whose non zero elements is hypercyclic finally we explore some connections with dynamics many of the hypercyclic operators discussed here are in at least one of the commonly accepted senses of the word chaotic

how to get universal inner functions we characterize a property that is useful for constructing large spaces of universal functions in a wide variety of settings in particular we show that given any sequence of automorphisms of the ball that admits a universal function f in h infty b n there exists a closed infinite dimensional subspace generated by inner functions that is isometric to ell 1 we put our results in the context of bounded symmetric domains

strong ergodic properties of a first order partial differential equation on etudie l equation differentielle d ordre 1 u t c x u x f x u pour t x 0 0 1 avec la condition initiale u 0 x v x pour x 0 1 on demontre l existence d une mesure invariante exacte ayant certaines proprietes supplementaires

universal entire functions for affine endomorphisms of c n abstract in this paper the affine endomorphisms of c n which support compositionally universal entire functions are completely characterized

on brondsted rockafellar s theorem for convex lower semicontinuous epi pointed functions in locally convex spaces in this work we give an extension of the brondsted rockafellar theorem and some of its important consequences to proper convex lower semicontinuous epi pointed functions defined in locally convex spaces we use a new approach based on a simple variational principle which also allows recovering the classical results in a natural way

a generalization of universal taylor series in simply connected domains abstract let be a simply connected proper subdomain of the complex plane and z 0 be a point in it is known that there are holomorphic functions f on for which the partial sums s n f z 0 of the taylor series about z 0 have universal approximation properties outside in this paper we investigate what can be said for the sequence n s n f z 0 when n is a sequence of complex numbers we also study a related analogue of a classical theorem of seleznev concerning the case where the radius of convergence of the universal power series is zero

spectral theory and hypercyclic subspaces a vector x in a hilbert space h is called hypercyclic for a bounded operator t h h if the orbit tnx n 1 is dense in h our main result states that if t satisfies the hypercyclicity criterion and the essential spectrum intersects the closed unit disk then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t the converse is true even if t is a hypercyclic operator which does not satisfy the hypercyclicity criterion as a consequence other characterizations are obtained for an operator t to have an infinite dimensional closed subspace of hypercyclic vectors these results apply to most of the hypercyclic operators that have appeared in the literature in particular they apply to bilateral and backward weighted shifts perturbations of the identity by backward weighted shifts multiplication operators and composition operators the main result also applies to the differentiation operator and the translation operator t f z f z 1 defined on certain hilbert spaces consisting of entire functions we also obtain a spectral characterization of the norm closure of the class of hypercyclic operators which have an infinite dimensional closed subspace of hypercyclic vectors

bifurcation control via state feedback for systems with a single uncontrollable mode the state feedback control of bifurcations with quadratic or cubic degeneracy is addressed for systems with a single uncontrollable mode based on normal forms and invariants the classification of bifurcations for systems with a single uncontrollable mode is obtained table 1 using invariants stability characterizations are derived for a family of bifurcations including saddle node bifurcations transcritical bifurcations pitchfork bifurcations and bifurcations with a cusp or hysteresis phenomenon bifurcations in systems under perturbed feedbacks are also addressed in the case of a saddle node bifurcation continuous but not differentiable feedbacks are introduced to locally remove the bifurcation and to achieve the stability

on a universality property of certain integral operators in this paper we establish a universality property of fourier and hankel convolution operators and dunkl transforms

analysis and control of hopf bifurcations in this paper control systems with two uncontrollable modes on the imaginary axis are studied the main contributions include the local orientation control of periodic solutions and center manifolds the quadratic normal form of systems with two imaginary uncontrollable modes the stabilization of the hopf bifurcation by state feedback and the quadratic invariants that characterize the nonlinearity of a system and its hopf bifurcation

distributed control design for parabolic evolution equations application to compressor stall control we present a theoretical study of distributed control design for semilinear parabolic nonlocal evolution equations with an application to axial compressor stall control using air injection by taking advantage of the spatial invariance of the equations a linear controller is constructed following bamieh et al via linear quadratic control of each fourier mode we derive sufficient conditions for the linear controller to stabilize the full nonlinear system concepts such as controller decentralization finite dimensional implementation inverse optimality and beneficial nonlinearities are discussed in the second part of this paper these developments are applied to a model of axial compressor control with air injection the unactuated model is derived following the work of moore and greitzer and the model coupled with air injection actuation follows the works of behnken et al and weigl et al a numerical study of the control designs is pursued and the comparison of controller performance is discussed the techniques presented here are expected to be useful for distributed control design of a much broader class of nonlinear reaction diffusion systems

non sequential weak supercyclicity and hypercyclicity abstract a bounded linear operator t acting on a banach space b is called weakly hypercyclic if there exists x b such that the orbit t n x n 0 1 is weakly dense in b and t is called weakly supercyclic if there is x b for which the projective orbit t n x c n 0 1 is weakly dense in b if weak density is replaced by weak sequential density then t is said to be weakly sequentially hypercyclic or supercyclic respectively it is shown that on a separable hilbert space there are weakly supercyclic operators which are not weakly sequentially supercyclic this is achieved by constructing a borel probability measure on the unit circle for which the fourier coefficients vanish at infinity and the multiplication operator m f z z f z acting on l 2 is weakly supercyclic it is not weakly sequentially supercyclic since the projective orbit under m of each element in l 2 is weakly sequentially closed this answers a question posed by bayart and matheron it is proved that the bilateral shift on l p z 1 p is weakly supercyclic if and only if 2 p and that any weakly supercyclic weighted bilateral shift on l p z for 1 p 2 is norm supercyclic it is also shown that any weakly hypercyclic weighted bilateral shift on l p z for 1 p 2 is norm hypercyclic which answers a question of chan and sanders