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

distributional chaos for operators on banach spaces abstract four notions of distributional chaos namely dc1 dc2 dc 2 1 2 and dc3 are studied within the framework of operators on banach spaces it is known that for general dynamical systems dc1 dc2 dc 2 1 2 dc3 we show that dc1 and dc2 coincide in our context which answers a natural question in contrast there exist dc 2 1 2 operators which are not dc2 under the condition that there exists a dense set x 0 x such that t n x 0 for any x x 0 dc3 operators are shown to be dc1 moreover we prove that any upper frequently hypercyclic operator is dc 2 1 2 finally several examples are provided to distinguish between different notions of distributional chaos li yorke chaos and irregularity

distributional chaos for linear operators abstract we characterize distributional chaos for linear operators on frechet spaces in terms of a computable condition dcc and also as the existence of distributionally irregular vectors a sufficient condition for the existence of dense uniformly distributionally irregular manifolds is presented which is very general and can be applied to many classes of operators distributional chaos is also analyzed in connection with frequent hypercyclicity and the particular cases of weighted shifts and composition operators are given as an illustration of the previous results

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

brownian motion in a wedge with oblique reflection this work is concerned with the existence and uniqueness of a strong markov process that has continuous sample paths and the following additional properties i the state space is an infinite two dimensional wedge and the process behaves in the interior of the wedge like an ordinary brownian motion ii the process reflects instantaneously at the boundary of the wedge the angle of reflection being constant along each side iii the amount of time that the process spends at the comer of the wedge is zero i e the set of times for which the process is at the comer has lebesgue measure zero hereafter let be the angle of the wedge 0 2 let 1 and 2 be the angles of reflection on the two sides of the wedge measured from the inward normals the positive angles being toward the corner 1 2 and set 1 2 the question of existence and uniqueness is recast as a submartingale problem in the style used by stroock and varadhan diffusion processes with boundary conditions comm pure appl math 24 1971 pp 147 225 for diffusions on smooth domains with smooth boundary conditions it is shown that no solution exists if 2 in this case there is a unique continuous strong markov process satisfying i ii above it reaches the corner of the wedge almost surely and it remains there if 2 however then there is a unique continuous strong markov process statisfying i iii it is shown that starting away from the corner this process does not reach the corner of the wedge if 0 and does reach the corner if 0 2 the general theory of multi dimensional diffusions does not apply to the above problem because in general the boundary of the state space is not smooth and there is a discontinuity in the direction of reflection at the corner for some values of the process arises from diffusion approximations to storage systems and queueing networks i the state space is an infinite two dimensional wedge and the process behaves in the interior of the wedge like an ordinary brownian motion ii the process reflects instantaneously at the boundary of the wedge and the angle of reflection being constant along each side iii the amount of time that the process spends at the corner of the wedge is zero i e the set of times for which the process is at the corner has lebesgue measure zero

genericity of wild holomorphic functions and common hypercyclic vectors abstract let t be the translation operator by in the space of entire functions h c defined by t f z f z we prove that there is a residual set g of entire functions such that for every f g and every c 0 the sequence t n f is dense in h c that is g is a residual set of common hypercyclic vectors functions for the family t c 0 also we prove similar results for many families of operators as multiples of differential operator multiples of backward shift weighted backward shifts

hilbert transform and its engineering applications the hilbert transform is useful in calculating instantaneous attributes of a time series especially the envelope amplitude and instantaneous frequency the instantaneous envelope is the amplitude of the complex hilbert transform the instantaneous frequency is the time rate of change of the instantaneous phase angle these properties can be applied to identify dynamic characteristics of a linear as well as a nonlinear system however the conventional discrete hilbert transform which is based on fast fourier transform and inverse fourier transform has shown the lack of accuracy for time derivative calculations in this paper we first introduce the hilbert transform and its applications to the nonlinear system parameter identification then we address the practical issues in applying the hilbert transform to engineering applications to increase the accuracy of the envelope detection we propose a hilbert transform technique based on local maxima interpolation analyses and simulations are carried out to demonstrate the advantages of the proposed technique finally we employ the proposed local maxima interpolation technique in identifying the nonlinear dynamic characteristics of industrial examples

the fourier decomposition method for nonlinear and non stationary time series analysis for many decades there has been a general perception in the literature that fourier methods are not suitable for the analysis of nonlinear and non stationary data in this paper we propose a novel and adaptive fourier decomposition method fdm based on the fourier theory and demonstrate its efficacy for the analysis of nonlinear and non stationary time series the proposed fdm decomposes any data into a small number of fourier intrinsic band functions fibfs the fdm presents a generalized fourier expansion with variable amplitudes and variable frequencies of a time series by the fourier method itself we propose an idea of zero phase filter bank based multivariate fdm mfdm for the analysis of multivariate nonlinear and non stationary time series using the fdm we also present an algorithm to obtain cut off frequencies for mfdm the proposed mfdm generates a finite number of band limited multivariate fibfs mfibfs the mfdm preserves some intrinsic physical properties of the multivariate data such as scale alignment trend and instantaneous frequency the proposed methods provide a time frequency energy tfe distribution that reveals the intrinsic structure of a data numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms

common hypercyclic vectors for the unitary orbit of a hypercyclic operator abstract for a separable infinite dimensional hilbert space it was recently shown by the authors that the similarity orbit of a hypercyclic operator contains a path of operators which is dense in the operator algebra with the strong operator topology and yet the set of common hypercyclic vectors for the entire path is a dense g set motivated by that result we show in the present paper that the unitary orbit of any hypercyclic operator contains a path of operators whose closure contains the entire unitary orbit with the strong operator topology and yet every nonzero vector in the linear span of the orbit of a given hypercyclic vector is a common hypercyclic vector for the entire path

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

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

non linear free vibration identification via the hilbert transform a time domain non parametric method for non linear vibration system identification based on the hilbert transform is introduced the method is demonstrated using computer simulations of different types of non linear elastic and damping dynamic systems

topologically transitive extensions of bounded operators let x be any banach space and t a bounded operator on x an extensionopen image in new window of the pair x t consists of a banach space open image in new window in which x embeds isometrically through an isometry i and a bounded operatoropen image in new window on open image in new window such that open image in new window when x is separable it is additionally required that open image in new window be separable we say that open image in new window is a topologically transitive extension of x t when open image in new window is topologically transitive on open image in new window i e for every pair open image in new window of non empty open subsets of open image in new window there exists an integer n such that open image in new window is non empty we show that any such pair x t admits a topologically transitive extension open image in new window and that when h is a hilbert space h t admits a topologically transitive extension open image in new window where open image in new window is also a hilbert space we show that these extensions are indeed chaotic

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

identification of weakly nonlinearities in multiple coupled oscillators this paper considers the analysis of free nonlinear response of multi degree of freedom mdof vibration systems demonstrating that system skeleton curves are significantly changed in the presence of coupling the hilbert transform vibration decomposition together with the modal spatial coordinate transform allow precise identification of initial nonlinear characteristics

the reflection map with discontinuities we study the multidimensional reflection map on the spacesd 0 t r k andd 0 8 r k of right continuous r k valued functions on 0 t or 0 8 with left limits endowed with variants of the skorohod 1956 m1 topology the reflection map was used with the continuous mapping theorem by harrison and reiman 1981 and reiman 1984 to establish heavy traffic limit theorems with reflected brownian motion limit processes for vector valued queue length waiting time and workload stochastic processes in single class open queueing networks since brownian motion and reflected brownian motion have continuous sample paths the topology of uniform convergence over bounded intervals could be used for those results variants of them1 topologies are needed to obtain alternative discontinuous limits approached gradually by the converging processes as occurs in stochastic fluid networks with bursty exogenous input processes e g with on off sources having heavy tailed on periods or off periods having infinite variance we show that the reflection map is continuous at limits without simultaneous jumps of opposite sign in the coordinate functions provided that the productm1 topology is used as a consequence the reflection map is continuous with the productm1 topology at all functions that have discontinuities in only one coordinate at a time that continuity property also holds for more general reflection maps and is sufficient to support limit theorems for stochastic processes in most applications we apply the continuity of the reflection map to obtain limits for buffer content stochastic processes in stochastic fluid networks

unimodular eigenvalues uniformly distributed sequences and linear dynamics we study increasing sequences of positive integers nk k 1 with the following property every bounded linear operator t acting on a separable banach or hilbert space with supk 1 tnk has a countable set of unimodular eigenvalues whether this property holds or not depends on the distribution modulo one of sequences nk k 1 r or on the growth of nk 1 nk counterexamples to some conjectures in linear dynamics are given for instance a hilbert space operator which is frequently hypercyclic chaotic but not topologically mixing is constructed the situation of c0 semigroups is also discussed

the role of the angle in supercyclic behavior abstract a bounded operator t acting on a hilbert space h is said to be supercyclic if there is a vector f h such that the projective orbit t n f n 0 and c is dense in h we use a new method based on a very simple geometric idea that allows us to decide whether an operator is supercyclic or not the method is applied to obtain the following result a composition operator acting on the hardy space whose inducing symbol is a parabolic linear fractional map of the disk onto a proper subdisk is not supercyclic this result finishes the characterization of the supercyclic behavior of composition operators induced by linear fractional maps and thus completes previous work of bourdon and shapiro

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

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

vibration signal component separation by iteratively using basis pursuit and its application in mechanical fault detection abstract using different transform basis the vibration signal components such as impulses harmonics and modulated components can be effectively separated by basis pursuit for multicomponent vibration signals this paper proposes a new vibration signal component separation approach by iteratively using basis pursuit the signal is firstly denoised by basis pursuit denoising and the impulsive component can be separated by using identity matrix and redundant fourier basis then signal components with different frequency ranges can be separated by using short time fourier transform basis with different window lengths and the components with high frequency are separated after each iteration to choose the best basis from the dictionary the separation coefficient is proposed for evaluating the separating performance of the transform basis the proposed approach empirical mode decomposition emd and matching pursuit are respectively applied to analyzing a simulated faulty vibration and a simulated faulty gear vibration signal the comparison results demonstrate its superiority to emd and matching pursuit in separation accuracy finally the proposed approach is used for detecting the faults of a rotor and rolling bearings the results further show that this proposed method can be effectively applied to mechanical fault diagnosis

hilbertian jamison sequences and rigid dynamical systems a strictly increasing sequence nk k 0 of positive integers is said to be a hilbertian jamison sequence if for any bounded operator t on a separable hilbert space such that supk 0 tnk the set of eigenvalues of modulus 1 of t is at most countable we first give a complete characterization of such sequences we then turn to the study of rigidity sequences nk k 0 for weakly mixing dynamical systems on measure spaces and give various conditions some of which are closely related to the jamison condition for a sequence to be a rigidity sequence we obtain on our way a complete characterization of topological rigidity and uniform rigidity sequences for linear dynamical systems and we construct in this framework examples of dynamical systems which are both weakly mixing in the measure theoretic sense and uniformly rigid

open queueing networks in heavy traffic this paper presents heavy traffic limit theorems for the queue length and sojourn time processes associated with open queueing networks these limit theorems state that properly normalized sequences of queue length and sojourn time processes converge weakly to a certain diffusion as the network traffic intensity converges to unity the limit diffusion is reflected brownian motion on the nonnegative orthant this process behaves like brownian motion on the interior of its state space and reflects instantaneously on the boundaries the reflection direction is a constant for each boundary hyperplane

common hypercyclic vectors for the conjugate class of a hypercyclic operator abstract given a separable in nite dimensional hilbert space it was recently shown by the authors that there is a path of chaotic operators which is dense in the operator algebra with the strong operator topology and along which every operator has the exact same dense set of hypercyclic vectors in the present work we show that the conjugate set of any hypercyclic operator on a separable in nite dimensional banach space always contains a path of operators which is dense with the strong operator topology and yet the set of common hypercyclic vectors for the entire path is a dense set as a corollary the hypercyclic operators on such a banach space form a connected subset of the operator algebra with the strong operator topology 1 introduction throughout the present paper let be a separable in nite dimensional banach space over the scalar eld or and let denote the algebra of bounded linear operators an operator in is hypercyclic if there is a vector in for which its orbit 0 is dense in such a vector is called a hypercyclic vector for an operator in is hypercyclic if and only if the set of hypercyclic vectors for denoted by is a dense set see kitai 23 for a countable family of hypercyclic operators a direct application of the baire category theorem implies that the set

reflected brownian motion with skew symmetric data in a polyhedral domain this paper is concerned with the characterization and invariant measures of certain reflected brownian motions rbm s in polyhedral domains the kind of rbm studied here behaves like d dimensional brownian motion with constant drift in the interior of a simple polyhedron and is instantaneously reflected at the boundary in directions that depend on the face that is hit under the assumption that the directions of reflection satisfy a certain skew symmetry condition first introduced in harrison williams 9 it is shown that such an rbm can be characterized in terms of a family of submartingales and that it reaches non smooth parts of the boundary with probability zero in 9 a purely analytic problem associated with such an rbm was solved here the exponential form solution obtained in 9 is shown to be the density of an invariant measure for the rbm furthermore if the density is integrable over the polyhedral state space then it yields the unique stationary distribution for the rbm in the proofs of these results a key role is played by a dual process for the rbm and by results in 9 for reflected brownian motions on smooth approximating domains

remarks on common hypercyclic vectors abstract we treat the question of existence of common hypercyclic vectors for families of continuous linear operators it is shown that for any continuous linear operator t on a complex frechet space x and a set r c which is not of zero three dimensional lebesgue measure the family a t b i a b has no common hypercyclic vectors this allows to answer negatively questions raised by godefroy and shapiro and by aron we also prove a sufficient condition for a family of scalar multiples of a given operator on a complex frechet space to have a common hypercyclic vector it allows to show that if d z c z 1 and h d is non constant then the family z m b 1 z a 1 has a common hypercyclic vector where m h 2 d h 2 d m f f a inf z z d and b sup z z d providing an affirmative answer to a question by bayart and grivaux finally extending a result of costakis and sambarino we prove that the family a t b a b c 0 has a common hypercyclic vector where t b f z f z b acts on the frechet space h c of entire functions on one complex variable

sums of hypercyclic operators abstract every bounded operator on a complex infinite dimensional separable hilbert space can be written as the sum of two hypercyclic operators and also as the sum of two chaotic operators

a boundary property of semimartingale reflecting brownian motions we consider a class of reflecting brownian motions on the non negative orthant inr k in the interior of the orthant such a process behaves like brownian motion with a constant covariance matrix and drift vector at each of the k 1 dimensional faces that form the boundary of the orthant the process reflects instantaneously in a direction that is constant over the face we give a necessary condition for the process to have a certain semimartingale decomposition and then show that the boundary processes appearing in this decomposition do not charge the set of times that the process is at the intersection of two or more faces this boundary property plays an essential role in the derivation performed in a separate work of an analytical characterization of the stationary distributions of such semimartingale reflecting brownian motions

variational mode decomposition during the late 1990s huang introduced the algorithm called empirical mode decomposition which is widely used today to recursively decompose a signal into different modes of unknown but separate spectral bands emd is known for limitations like sensitivity to noise and sampling these limitations could only partially be addressed by more mathematical attempts to this decomposition problem like synchrosqueezing empirical wavelets or recursive variational decomposition here we propose an entirely non recursive variational mode decomposition model where the modes are extracted concurrently the model looks for an ensemble of modes and their respective center frequencies such that the modes collectively reproduce the input signal while each being smooth after demodulation into baseband in fourier domain this corresponds to a narrow band prior we show important relations to wiener filter denoising indeed the proposed method is a generalization of the classic wiener filter into multiple adaptive bands our model provides a solution to the decomposition problem that is theoretically well founded and still easy to understand the variational model is efficiently optimized using an alternating direction method of multipliers approach preliminary results show attractive performance with respect to existing mode decomposition models in particular our proposed model is much more robust to sampling and noise finally we show promising practical decomposition results on a series of artificial and real data

hypercyclicity and unimodular point spectrum abstract we show that an operator on a separable complex banach space with sufficiently many eigenvectors associated to eigenvalues of modulus 1 is hypercyclic we apply this result to construct hypercyclic operators with prescribed k unimodular point spectrum we show how eigenvectors associated to unimodular eigenvalues can be used to exhibit common hypercyclic vectors for uncountable families of operators and prove that the family of composition operators c on h 2 d where is a disk automorphism having 1 as attractive fixed point has a residual set of common hypercyclic vectors

a synchrosqueezed wavelet transform enhanced by extended analytical mode decomposition method for dynamic signal reconstruction abstract a synchrosqueezed wavelet transform combined by wavelet analysis and time frequency reallocation method was recently developed to improve the quality of time frequency representation and construct the components of a signal however the quality of this transform highly depends on the parameters of wavelet functions to overcome the effects of wavelet function parameters on signal decomposition an analytical mode decomposition method was proposed to reconstruct each component the analytical mode decomposition selects the bisecting frequency between any two adjacent instantaneous frequencies estimated from a preliminary synchrosqueezed wavelet analysis and analytically extracts the individual components from a signal between any two bisecting frequencies two examples including a frequency modulated amplitude decayed signal and seismic responses of a two story building are analyzed it is demonstrated that the analytically derived components are insensitive to the selection parameters of wavelet function and bisecting frequency the proposed method is superior to the synchrosqueezed wavelet transform method for dynamic signal reconstruction

frequently hypercyclic operators we investigate the subject of linear dynamics by studying the notion of frequent hypercyclicity for bounded operators t on separable complex f spaces t is frequently hypercyclic if there exists a vector x such that for every nonempty open subset u of x the set of integers n such that t n x belongs to u has positive lower density we give several criteria for frequent hypercyclicity and this leads us in particular to study linear transformations from the point of view of ergodic theory several other topics which are classical in hypercyclicity theory are also investigated in the frequent hypercyclicity setting

time varying vibration decomposition and analysis based on the hilbert transform this paper introduces a simple method for time varying vibration decomposition based on the hilbert transform the non stationary frequency of the largest component is estimated as an average function of the instantaneous frequency of the composition and the corresponding envelope is estimated according to synchronous demodulation the method is demonstrated using computer simulation of different types of non stationary and nonlinear vibration

a hypercyclic finite rank perturbation of a unitary operator a unitary operator v and a rank 2 operator r acting on a hilbert space mathcal h are constructed such that v r is hypercyclic this answers affirmatively a question of salas whether a finite rank perturbation of a hyponormal operator can be supercyclic

reflected brownian motion on an orthant we consider a k dimensional diffusion process z whose state space is the nonnegative orthant on the interior of the orthant z behaves like a kdimensional brownian motion with arbitrary covariance matrix and drift vector at each of the k 1 dimensional hyperplanes that form the boundary of the orthant z reflects instantaneously in a direction that is constant over that hyperplane there is no extant theory of multidimensional diffusion that applies to this process because the boundary of its state space is not smooth we adopt an approach that requires a restriction on the directions of reflection but reiman has shown that this restriction is met by all diffusions z arising as heavy traffic limits in open k station queuing networks our process z is defined as a path to path mapping of k dimensional brownian motion from this construction it follows that z is a continuous markov process and a semimartingale using the latter property we obtain a change of variable formula from which one can develop a complete analytical theory for the process z

strong mixing measures for linear operators and frequent hypercyclicity abstract we construct strongly mixing invariant measures with full support for operators on f spaces which satisfy the frequent hypercyclicity criterion for unilateral backward shifts on sequence spaces a slight modification shows that one can even obtain exact invariant measures

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

on the distribution of multidimensional reflected brownian motion let z z t t 0 be a reflected brownian motion on the k dimensional nonnegative orthant with the direction of reflection constant over each boundary surface such processes arise in heavy traffic theory for k station networks of queues this paper continues our study of the diffusion process z with attention restricted to the case k 2 for simplicity most of the results extend directly to higher dimensions our notation and style of argument are designed to suggest appropriate generalizations for arbitrary k wherever possible the backward equation for the transition density function with boundary and initial conditions the corresponding forward equation and the equation for the steady state distribution are all derived informally also presented are various calculations relating to steady state distributions including a moment formula and the derivation of a condition involving the drifts and directions of reflection that we conjecture to be necessary and sufficient for existence

discrete flow networks bottleneck analysis and fluid approximations we conduct bottleneck analysis of a deterministic dynamic discrete flow network the analysis presupposes only the existence of long run averages and is based on a continuous fluid approximation to the network in terms of these averages the results provide functional strong laws of large numbers for stochastic jackson queueing networks since they apply to their sample paths with probability one