相关论文: Stochastic-like behaviour in nonuniformly expandin…

Random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniformly continuous and contractive are considered. A non-degeneracy and a…

For non-uniformly expanding maps inducing with a general return time to Gibbs Markov maps, we provide sufficient conditions for obtaining higher order asymptotics for the correlation function in the infinite measure setting. Along the way,…

It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the…

A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain a Langevin type…

We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to…

We derive Markovian master equations of single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding Markovian master equations with exact…

Inspired by theories such as Loop Quantum Gravity, a class of stochastic graph dynamics was studied in an attempt to gain a better understanding of discrete relational systems under the influence of local dynamics. Unlabeled graphs in a…

The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their…

We investigate linear parabolic maps on the torus. In a generic case these maps are non-invertible and discontinuous. Although the metric entropy of these systems is equal to zero, their dynamics is non-trivial due to folding of the image…

This paper discusses the evolution of probability distributions for certain time-dependent dynamical systems. Exponential loss of memory is proved for expanding maps and for one-dimensional piecewise expanding maps with slowly varying…

We identify a set of dynamical maps of open quantum system, and refer to them as "$ \epsilon $-Markovian" maps. It is constituted of maps which, in a higher dimensional system-environment Hilbert space, possibly violate Born approximation…

We consider the time dependent probability distribution of a coarse grained observable Y whose evolution is governed by a discrete time map. If the map is mixing, the time dependent one-step transition probabilities converge in the long…

We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…

General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General…

We continue the development of transfer operator techniques for expanding maps on a lattice coupled by general interaction functions. We obtain a spectral gap for an appropriately defined transfer operator, and, as corollaries, the…

In this work, we consider i.i.d. random perturbations of contracting Lorenz maps sufficiently close to a Rovella parameter. We prove that the quenched correlations of the random dynamical system decay exponentially.

The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…

We present here a general iterative formula which gives a (formal) series expansion for the time autocorrelation of smooth dynamical variables, for all Hamiltonian systems endowed with an invariant measure. We add some criteria, theoretical…

We present an analysis of one-dimensional models of dynamical systems that possess 'coherent structures'; global structures that disperse more slowly than local trajectory separation. We study cocycles generated by expanding interval maps…

Linked-twist maps are area-preserving, piece-wise diffeomorphisms, defined on a subset of the torus. They are non-uniformly hyperbolic generalisations of the well-known Arnold Cat Map. We show that a class of canonical examples have…