gibb s functionals on subshifts we consider functionals on one dimensional subshifts which have prescribed randon nikodym derivative under transportation by conjugating homeomorphisms and investigate their relation to ruelle s transfer operator in particular we show that two sided functionals essentially are products of a functional which are supported on stable and unstable leaves we also prove the meromorphicity of the fourier transform of correlation functions for axioma follows in a more general setting

convergence of dynamical zeta functions i study poles and zeros of zeta functions in one dimensional maps numerical and analytical arguments are given to show that the first pole of one such zeta function is given by the first zero ofanother zeta function this describes convergence of the calculations of the first zero which is generally the physically interesting quantity some remarks on how these results should generalize to zeta functions of dynamical systems with pruned symbolic dynamics and in higher dimensions follow

spectral statistics for unitary transfer matrices of binary graphs quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits it is proposed here to generalize this approach by considering arbitrary directed graphs with unitary transfer matrices an exponentially increasing contribution to the form factor is identified when performing a diagonal summation over periodic orbit degeneracy classes a special class of graphs so called binary graphs is studied in more detail for these the conditions for periodic orbit pairs to be correlated including correlations due to the unitarity of the transfer matrix can be given explicitly using combinatorial techniques it is possible to perform the summation over correlated periodic orbit pair contributions to the form factor for some low dimensional cases gradual convergence towards random matrix results is observed when increasing the number of vertices of the binary graphs

spectral decomposition of the renyi map the authors construct a generalized spectral decomposition of the frobenius perron operator of the general beta adic renyi map using a general iterative operator method applicable in principle to any mixing dynamical system they also explicitly define appropriate rigged hilbert spaces which provide mathematical meaning to the formally obtained spectral decomposition the explicit construction of the eigenvalues and eigenvectors allows one to show that the essential spectral radius of the frobenius perron operator decreases as the smoothness of the domain increases the reason for the change of the spectrum from the unit disk to isolated eigenvalues is the existence of coherent states of the frobenius perron operator which are not infinitely differentiable

the quest for the ultimate anisotropic banach space we present a new scale u t s p with s t 0 and 1 le p infty of anisotropic banach spaces defined via paley littlewood on which the transfer operator associated to a hyperbolic dynamical system has good spectral properties when p 1 and t is an integer the spaces are analogous to the geometric spaces considered by gou ezel and liverani when p 1 and 1 1 p s t 0 t 1 p the spaces are somewhat analogous to the geometric spaces considered by demers and liverani in addition just like for the microlocal spaces defined by baladi tsujii the spaces u t s p are amenable to the kneading approach of milnor thurson to study dynamical determinants and zeta functions

geometric algebra and the causal approach to multiparticle quantum mechanics it is argued that geometric algebra in the form of the multiparticle spacetime algebra is well suited to the study of multiparticle quantum theory with advantages over conventional techniques both in ease of calculation and in providing an intuitive geometric understanding of the results this is illustrated by comparing the geometric algebra approach for a system of two spin 1 2 particles with the nonrelativistic approach of holland phys rep 169 294 1988

alpha trimmed means and their relationship to median filters suppose that x is a finite set of n numbers the trimmed mean of x is obtained by sorting x into ascending order removing trimming a fixed fraction alpha 0 leq alpha leq 0 5 from the high and low ends of the sorted set and computing the average of the remaining values when applied to a sliding window of length lw the trimming process is called trim filtering for 0 5 the trimmed mean of a set is the median of the set and the filtering operation is called median filtering repeated application of a median filter to the output of a previous median filter of the same length lw eventually produces a signal which is invariant to median filtering this final signal is called the root signal this paper explains the relationship between trimmed means and median filters derives a simple straightforward and fast algorithm for applying a median filter and provides a new explanation of the convergence of repeated median filtering to the root signal the latter result incorporates an approach which permits generalization of the associated concepts to a larger class of index map filters

a markov partition that reflects the geometry of a hyperbolic toral automorphism we show how to construct a markov partition that reflects the geometrical action of a hyperbolic automorphism of the n torus the transition matrix is the transpose of the matrix induced by the automorphism in u dimensional homology provided this is non negative here u denotes the expanding dimension that condition is satisfied at least for some power of the original automorphism under a certain non degeneracy condition on the galois group of the characteristic polynomial the nu rectangles are constructed by an iterated function system and they resemble the product of the projection of a u dimensional face of the unit cube onto the unstable subspace and the projection of minus the orthogonal n u dimensional face onto the stable subspace

gibbs measures and power spectra for type i intermittent maps abstract gibbs measures of dynamical systems are investigated using the corresponding correlation function and power spectrum the method is shown to be equivalent to the concept of order q power spectra which has been developed previously a technique for the computation of these spectra is presented as an application we specially focus on the treatment of type i intermittent model maps and investigate their phase transition in the vicinity of the phase transition point the order q power spectra are shown to obey some typical scaling relation which is captured neither by the topological pressure nor by the ordinary power spectrum

periodic orbit expansions for classical smooth flows the authors derive a generalized selberg type zeta function for a smooth deterministic flow which relates the spectrum of an evolution operator to the periodic orbits of the flow this relation is a classical analogue of the quantum trace formulae and selberg type zeta functions

quantum scars of classical closed orbits in phase space the way in which quantum eigenstates are influenced by the closed orbits of a chaotic classical system is analysed in phase space x q p through the spectral wigner function w x e this is a sum over wigner functions of eigenstates within a range of energy e in the classical limit w is concentrated on the energy surface and smoothly distributed over it closed orbits provide oscillatory corrections scars for which explicit semiclassical formulae are calculated each scar is a fringe pattern decorating the orbit as x moves off the energy surface the fringes form an airy pattern with spacing of order h as x moves off the closed orbit the fringes form a complex gaussian with spacing h

noncommutative algebras for hyperbolic diffeomorphisms the gibbs states of classical equilibrium statistical mechanics can be extended to states on non commutative algebras satisfying the kubo martin schwinger boundary condition this way of looking at gibbs states is applied here to the study of differentiable dynamical systems when some strong or weak hyperbolicity conditions are satisfied

lyapunov exponents and anomalous diffusion of a lorentz gas with infinite horizon using approximate zeta functions we compute the lyapunov exponent the generalized lyapunov exponents and the diffusion constant for a lorentz gas on a square lattice thus having infinite horizon approximate zeta functions written in terms of probabilities rather than periodic orbits are used in order to avoid the convergence problems of cycle expansions the emphasis is on the relation between the analytic structure of the zeta function where a branch cut plays an important role and the asymptotic dynamics of the system the lyapunov exponent for the corresponding map agrees with the conjectured limit map 2 log r c o r and we derive an approximate value for the constantc in good agreement with numerical simulations we also find a diverging diffusion constantd t logt and a phase transition for the generalized lyapunov exponents

a theoretical analysis of the properties of median filters necessary and sufficient conditions for a signal to be invariant under a specific form of median filtering are derived these conditions state that a signal must be locally monotone to pass through a median filter unchanged it is proven that the form of successive median filtering of a signal i e the filtered output is itself again filtered eventually reduces the original signal to an invariant signal called a root signal for a signal of length l samples a maximum of frac 1 2 l 2 repeated filterings produces a root signal

locating resonances for axiom a dynamical systems for a class of differentiable dynamical systems called axiom a systems it has been shown by pollicott and the author that correlation functions have fourier transforms which are meromorphic in a strip the poles or resonances are however not easy to locate this note reviews the results which are known and discusses a simple model where the position of resonances can be estimated the effect of noise is also discussed

smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics this paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics we adopt a new point of view which has emerged progressively in recent years and which takes seriously into account the chaotic character of the microscopic time evolution the emphasis is on nonequilibrium steady states rather than the traditional approach to equilibrium point of view of boltzmann the nonequilibrium steady states in presence of a gaussian thermostat are described by srb measures in terms of these one can prove the gallavotti cohen fluctuation theorem one can also prove a general linear response formula and study its consequences which are not restricted to near equilibrium situations at equilibrium one recovers in particular the onsager reciprocity relations under suitable conditions the nonequilibrium steady states satisfy the pairing theorem of dettmann and morriss the results just mentioned hold so far only for classical systems they do not involve large size i e they hold without a thermodynamic limit

compact locally maximal hyperbolic sets for smooth maps fine statistical properties compact locally maximal hyperbolic sets are studied via geometrically defined functional spaces that take advantage of the smoothness of the map in a neighborhood of the hyperbolic set this provides a self contained theory that not only reproduces all the known classical results but also gives new insights on the statistical properties of these systems

geometric algebra and information geometry for quantum computational software abstract the art of quantum algorithm design is highly nontrivial grover s search algorithm constitutes a masterpiece of quantum computational software in this article we use methods of geometric algebra ga and information geometry ig to enhance the algebraic efficiency and the geometrical significance of the digital and analog representations of grover s algorithm respectively specifically ga is used to describe the grover iterate and the discretized iterative procedure that exploits quantum interference to amplify the probability amplitude of the target state before measuring the query register the transition from digital to analog descriptions occurs via stone s theorem which relates the unitary grover iterate to a suitable hermitian hamiltonian that controls schrodinger s quantum mechanical evolution of a quantum state towards the target state once the discrete to continuos transition is completed ig is used to interpret grover s iterative procedure as a geodesic path on the manifold of the parametric density operators of pure quantum states constructed from the continuous approximation of the parametric quantum output state in grover s algorithm finally we discuss the dissipationless nature of quantum computing recover the quadratic speedup relation and identify the superfluity of the walsh hadamard operation from an ig perspective with emphasis on statistical mechanical considerations

zeta functions and transfer operators for piecewise monotone transformations given a piecewise monotone transformationt of the interval and a piecewise continuous complex weight functiong of bounded variation we prove that the ruelle zeta function z of t g extends meromorphically to z 1 where lim g tn 1 g tg 1 n and thatz is a pole of if and only ifz 1 is an eigenvalue of the corresponding transfer operator l we do not assume that l leaves a reference measure invariant

on the thermodynamic approach towards time series analysis a scheme is presented which allows for the computation of the topological pressure and power spectra associated with equilibrium measures from a given time series its convergence properties are demonstrated on numerical data sets obtained from the lozi and the henon map numerical evidence for sharp peaks in the power spectrum of the non hyperbolic phase is given and supported by estimates using periodic orbit expansions

action correlations and random matrix theory the correlations in the spectra of quantum systems are intimately related to correlations which are of genuine classical origin and which appear in the spectra of actions of the classical periodic orbits of the corresponding classical systems we review this duality and the semiclassical theory which brings it about the conjecture that the quantum spectral statistics are described in terms of random matrix theory leads to the proposition that the classical two point correlation function is also given in terms of a universal function we study in detail the spectrum of actions of the baker map and use it to illustrate the steps needed to reveal the classical correlations their origin and their relation to symbolic dynamics

on survival dynamics of classical systems non chaotic open billiards abstract we report on decay problem of classical systems mesoscopic level consideration is given on the basis of transient dynamics of non interacting classical particles bounded in billiards three distinct decay channels are distinguished through the long tailed memory effects revealed by temporal behavior of survival probability t i the universal independent of geometry initial conditions and space dimension channel with 1 of brownian relaxation of non trapped regular parabolic trajectories and ii the non brownian channel 1 due to highly chaotic bouncing ball trajectories we develop a statistical approach to the problem earlier proposed for chaotic classical systems physica a 275 2000 70 a systematic coarse graining procedure is introduced for non chaotic systems exemplified by circle and square geometry which are characterized by a certain finite characteristic collision time we demonstrate how the transient dynamics is related to the intrinsic dynamics driven by the preserved liouville measure the detailed behavior of the late time survival probability including a role of the initial conditions and a system geometry is studied in detail both theoretically and numerically

billiards correlation functions we discuss various experiments on the time decay of velocity autocorrelation functions in billiards we perform new experiments and find results which are compatible with an exponential mixing hypothesis first put forward by friedman and martin fm they do not seem compatible with the stretched exponentials believed in spite of fm and more recently of chernov to describe the mixing the analysis leads to several byproducts we obtain information about the normal diffusive nature of the motion and we consider the probability distribution of the number of collisions in timetm astm finding a strong dependence on some geometric characteristics of the locus of the billiard obstacles

resonances in chaotic dynamics we present a discussion and some numerical results on the actual possibility of making accessible by numerical techniques the complex singularities of the power spectrum resonances for a chaotic signal henon s transformation is investigated in detail showing that the position of the leading resonance in the complex frequency plane determines the kind of mixing rate in the time evolution

on transfer operators for continued fractions with restricted digits for any non empty subset i of the natural numbers let lambda i denote those numbers in the unit interval whose continued fraction digits all lie in i define the corresponding transfer operator formula for formula where re rs theta i is the abscissa of convergence of the series formula when acting on a certain hilbert space hi rs we show that the operator li rs is conjugate to an integral operator ki rs if furthermore rs is real then ki rs is selfadjoint so that li rs hi rs hi rs has purely real spectrum it is proved that li rs also has purely real spectrum when acting on various hilbert or banach spaces of holomorphic functions on the nuclear space c omega 0 1 and on the frechet space c infty 0 1 the analytic properties of the map rs m li rs are investigated for certain alphabets i of an arithmetic nature for example i primes i squares i an arithmetic progression i the set of sums of two squares it is shown that rs m li rs admits an analytic continuation beyond the half plane re rs theta i

a generalization of median filtering using linear combinations of order statistics we consider a class of nonlinear filters whose output is given by a linear combination of the order statistics of the input sequence assuming a constant signal in white noise the coefficients in the linear combination are chosen to minimize the output mse for several noise distributions it is shown that the optimal order statistic filter osf tends toward the median filter as the noise becomes more impulsive the optimal osf is applied to an actual noisy image and is shown to perform well combining properties of both the averaging and median filters a more general design scheme for applications involving nonconstant signals is also given

on the effect of pruning on the singularity structure of zeta functions we investigate the topological zeta function for unimodal maps in general and dynamical zeta functions for the tent map in particular for the generic situation when the kneading sequence is aperiodic it is shown that the zeta functions have a natural boundary along its radius of convergence beyond which the function lacks analytic continuation we make a detailed study of the function n 0 1 z2n associated with sequences of period doublings it is demonstrated that this function has a dense set of singular points and zeros on the unit circle exhibiting a rich number theoretical structure

physical insight into superdiffusive dynamics of sinai billiard through collision statistics abstract we report on distinct steady motion dynamic regimes in chaotic sinai billiard sb a numerical study on elastic reflections from the sb boundary square wall of length l and circle obstacle of radius r is carried out for different r l the research is based on the exploration of the generalized diffusion equation and on the analysis of wall collision and the circle collision distributions observed at late times the asymptotes for the diffusion coefficient d r and the corresponding diffusion exponent z r are established for all geometries the universal r independent diffusion with d 1 t 1 3 and z 1 1 5 replaces the ballistic motion regime z 0 1 attributed to square billiard r 0 geometrically this superdiffusive regime is bounded by small radii 0 r r 1 r 1 l 2 4 when both diagonal and non diagonal bleher s corridors are open in the correspondent square lattice of lorentz gas lg model the relaxation dynamics observed is ensured by the universal diffusive propagation of the regular type and the bouncing ball type orbits within the random walk scheme this superdiffusive regime is due to the levy flights between the long distant scatterers with the increase in circle radius r 1 r r 2 r 2 l 2 the diagonal corridor closes but the arc touching effects continue to bring the long living bouncing ball orbits back to the non diagonal infinite corridors this transient non universal dynamics with 1 5 z r 2 also associated with the trapping of regular orbits seems to be characteristic of non fully hyperbolic billiard systems in sb with finite horizon r r 2 all the principal corridors are closed and the interplay between square and circle boundaries generates the known chaotic dynamics attributed to the fully hyperbolic systems this is also observed through the normal brownian diffusion z 2 2 and the gaussian statistics proved for both kinds of collisions

slow relaxation in weakly open rational polygons the interplay between the regular piecewise linear and irregular vertex angle boundary effects in nonintegrable rational polygonal billiards of m equal sides is discussed decay dynamics in polygons of perimeter p m and small opening delta is analyzed through the late time survival probability s m approximately equal t delta two distinct slow relaxation channels are established the primary universal channel exhibits relaxation of regular sliding orbits with delta 1 the secondary channel is given by delta 1 and becomes open when m p m delta it originates from vertex order disorder dual effects and is due to relaxation of chaoticlike excitations

spectral statistics in chaotic systems with a point interaction we consider quantum systems with a chaotic classical limit that are perturbed by a point like scatterer the spectral form factor k for these systems is evaluated semiclassically in terms of periodic and diffractive orbits it is shown for order 2 and 3 that off diagonal contributions to the form factor which involve diffractive orbits cancel exactly the diagonal contributions from diffractive orbits implying that the perturbation by the scatterer does not change the spectral statistic we further show that parametric spectral statistics for these systems are universal for small changes of the strength of the scatterer

dynamical averaging in terms of periodic orbits abstract periodic orbit theory methods for evaluation of average values of observables for chaotic dynamical systems are reviewed and illustrated by several examples such as evaluation of the lyapunov exponents and the diffusion constants

explicit eigenvalue estimates for transfer operators acting on spaces of holomorphic functions abstract we consider transfer operators acting on spaces of holomorphic functions and provide explicit bounds for their eigenvalues more precisely if is any open set in c d and l is a suitable transfer operator acting on bergman space a 2 its eigenvalue sequence n l is bounded by n l a exp a n 1 d where a a 0 are explicitly given

escape probability for classically chaotic systems abstract a statistical approach to study the escape of an ensemble of particles from classical chaotic systems is proposed the universal kinetic decay laws exponential and algebraic are found through the velocity angle distribution and shown to be specific of distinct motion regimes in the billiards with a small opening on the basis of the particular case of the dispersing sinai billiard the escape probability is given in explicit form and the temporal and geometrical conditions are enunciated to make controlled observations of decay dynamics in numerical experiments

algebraic and dirac hestenes spinors and spinor fields almost all presentations of dirac theory in first or second quantization in physics and mathematics textbooks make use of covariant dirac spinor fields an exception is the presentation of that theory first quantization offered originally by hestenes and now used by many authors there a new concept of spinor field as a sum of nonhomogeneous even multivectors fields is used however a careful analysis detailed below shows that the original hestenes definition cannot be correct since it conflicts with the meaning of the fierz identities in this paper we start a program dedicated to the examination of the mathematical and physical basis for a comprehensive definition of the objects used by hestenes in order to do that we give a preliminary definition of algebraic spinor fields asf and dirac hestenes spinor fields dhsf on minkowski space time as some equivalence classes of pairs u u where u is a spinorial frame field and u is an appropriate sum of multivectors fields to be specified below the necessity of our definitions are shown by a careful analysis of possible formulations of dirac theory and the meaning of the set of fierz identities associated with the bilinear covariants on minkowski space time made with asf or dhsf we believe that the present paper clarifies some misunderstandings past and recent appearing on the literature of the subject it will be followed by a sequel paper where definitive definitions of asf and dhsf are given as appropriate sections of a vector bundle called the left spin clifford bundle the bundle formulation is essential in order to be possible to produce a coherent theory for the covariant derivatives of these fields on arbitrary riemann cartan space times the present paper contains also appendixes a e which exhibits a truly useful collection of results concerning the theory of clifford algebras including many tricks of the trade necessary for the intelligibility of the text

one dimensional gibbs states and axiom a diffeomorphisms on etudie la mecanique statistique en equilibre de systemes reticules classiques a une dimension a interactions a decroissance exponentielle pour de tels systemes les transformees de fourier des fonctions de correlation de paires sont meromorphes dans une bande et les residus des poles peuvent s exprimer en termes de distributions de gibbs on applique ces resultats aux diffeomorphismes de l axiome a de smale

an estimation on the output mean value of median filtering at edge location median filtering is a simple and efficient method in signal processing examples show that it is better than the mean filtering in preserving edges until now however this property has not been proven in theory when a step edge having the values of h and h is corrupted by zero mean noise we guess that the output mean value of the median filtering at the first edge point lies in the interval h h l where l is the length of the filter window in this correspondence part of this problem is proven

correlation spectrum of quenched and annealed equilibrium states for random expanding maps we show that the integrated transfer operators for positively weighted independent identically distributed smooth expanding systems give rise to annealed equilibrium states for a new variational principle the unique annealed equilibrium state coincides with the unique annealed gibbs state using work of ruelle 1990 and fried 1995 on generalised fredholm determinants for transfer operators we prove that the discrete spectrum of the transfer operators coincides with the correlation spectrum of these invariant measures yielding exponential decay of correlations and with the poles of an annealed zeta function defined also for complex weights a modified integrated transfer operator is introduced which describes the relativised quenched states studied e g by kifer 1992 and conditions including srb ensuring coincidence of quenched and annealed states are given for small random perturbations we obtain stability results on the quenched and annealed measures and spectra by applying perturbative results of young and the author 1993

the thermodynamic formalism for expanding maps letf x x be an expanding map of a compact space small distances are increased by a factor 1 a generating function z is defined which countsf periodic points with a weight one can express in terms of nonstandard fredholm determinants of certain transfer operators which can be studied by methods borrowed from statistical mechanics in this paper we review the spectral properties of the transfer operators and the corresponding analytic properties of z gibbs distributions and applications to julia sets are also discussed some new results are proved and some natural conjectures are proposed

periodic orbit asymptotics for intermittent hamiltonian systems abstract we address the problems in applying cycle expansions to bound chaotic systems caused by intermittence and incompleteness of the symbolic dynamics we discuss zeta functions associated with weighted evolution operators and in particular a one parameter family of weights relevant for the calculation of classical resonance spectra semiclassical spectra and topological entropy for a bound intermittent system we discuss an approximation of the zeta function in terms of probabilities rather than cycle instabilities this approximation provides a generalization of the fundamental part of a cycle expansion to systems lacking a finite symbolic dynamics this approach is particularly suitable for determining asymptotic properties of periodic orbits which are essential for scrutinizing the semiclassical limit of gutzwiller s semiclassical trace formula the sinai billiard is used as model system in particular we develop a crude approximation of the semiclassical zeta function which turns out to possess nonanalytical features we also discuss the contribution to the semiclassical level density from the neutral orbits finally we discuss implications of our findings for the spectral form factor and compute the asymptotic behaviour of the spectral rigidity the result is found to be consistent with exact quantum mechanical calculations

moments of the wigner delay times the wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system for chaotic systems the statistics of the individual delay times whose average is the wigner time delay are thought to be well described by random matrix theory here we present a semiclassical derivation showing the validity of random matrix results in order to simplify the semiclassical treatment we express the moments of the delay times in terms of correlation functions of scattering matrices at different energies in the semiclassical approximation the elements of the scattering matrix are given in terms of the classical scattering trajectories requiring one to study correlations between sets of such trajectories we describe the structure of correlated sets of trajectories and formulate the rules for their evaluation to the leading order in inverse channel number this allows us to derive a polynomial equation satisfied by the generating function of the moments along with showing the agreement of our semiclassical results with the moments predicted by random matrix theory we infer that the scattering matrix is unitary to all orders in the semiclassical approximation

streaking in median filtered images this paper presents a probabilistic analysis of the streaking or blotching effect commonly observed in median filtered signals in both one and two dimensions the effcts are identified as runs of equal or nearly equal values which create visual impressions that have no visual correlate for one dimensional discrete iid random signals with continuous input probability densities the probability of a streak of length l occurring is computed and shown to be independent of the input probability distribution expressions for the first and second moments of the streak length are also derived and certain asymptotic results are given as the analysis and definition of the analogous effect in two dimensions is less tractable the probability that medians taken from distinct overlapping windows will take the same value is derived for various filter geometries the analytic results are supported by examples using both one and two dimensional signals

entire fredholm determinants for evaluation of semiclassical and thermodynamical spectra proofs that fredholm determinants of transfer operators for hyperbolic flows are entire can be extended to a large new class of multiplicative evolution operators we construct such operators both for the gutzwiller semiclassical quantum mechanics and for classical thermodynamic formalism and introduce a new functional determinant which is expected to be entire for axiom a flows and whose zeros coincide with the zeros of the gutzwiller voros zeta function

periodic orbits and a correlation function for the semiclassical density of states through the rule that there is one quantum state per planck cell in phase space classical mechanics supplies an average semiclassical density of states for a system with bound motion can it supply more refined averages such as the correlation function for the density of states i shall argue that for the two extreme cases of integrable classical motion and ergodic classical motion information can indeed be obtained on not quite this but a closely related correlation function the results for the two types of motion are markedly different

determination of resonance spectra for bound chaotic systems we consider the computation of the eigenvalues of the evolution operator the resonance spectrum by means of the zeros of a zeta function in particular we address the problems of applying this formalism to bound chaotic systems caused by e g intermittency and non completeness of the symbolic dynamics for bound intermittent systems we derive an approximation of the zeta function with the aid of this zeta function it is argued that bound systems with long time tails have branch cuts in the zeta function and traces of the evolution operator approaching unity as a power law we also show that the dominant time scale can be much longer than the period of the shortest periodic orbit as is for example the case for the hyperbola billiard isolated zeros of the zeta function for the hyperbola billiard are evaluated by means of a cycle expansion crucial for the success of this approach is the identification of a sequence of periodic orbit responsible for a logarithmic branch cut in the zeta function semiclassical implications are briefly discussed

median filtering by threshold decomposition median filters are a special class of ranked order filters used for smoothing signals repeated application of the filter on a quantized signal of finite length ultimately results in a sequence termed a root signal which is invariant to further passes of the median filter in this paper it is shown that median filtering an arbitrary level signal to its root is equivalent to decomposing the signal into binary signals filtering each binary signal to a root with a binary median filter and then reversing the decomposition this equivalence allows problems in the analysis and the implementation of median filters for arbitrary level signals to be reduced to the equivalent problems for binary signals since the effects of median filters on binary signals are well understood this technique is a powerful new tool

semiclassical form factor for spectral and matrix element fluctuations of multidimensional chaotic systems we present a semiclassical calculation of the generalized form factor kab tau which characterizes the fluctuations of matrix elements of the operators a and b in the eigenbasis of the hamiltonian of a chaotic system our approach is based on some recently developed techniques for the spectral form factor of systems with hyperbolic and ergodic underlying classical dynamics and f 2 degrees of freedom that allow us to go beyond the diagonal approximation first we extend these techniques to systems with f 2 then we use these results to calculate kab tau we show that the dependence on the rescaled time tau time in units of the heisenberg time is universal for both the spectral and the generalized form factor furthermore we derive a relation between kab tau and the classical time correlation function of the weyl symbols of a and b