Related papers: Unique ergodicity for noninvertible function syste…

We use a modification of the parameterization method to study invariant manifolds for difference equations. We establish existence, regularity, smooth dependence on parameters and study several singular limits, even if the difference…

We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…

In this paper, we study rotation numbers of random dynamical systems on the circle. We prove the existence of rotation numbers and the continuous dependence of rotation numbers on the systems. As an application, we prove a theorem on…

We study random walks on the integers driven by a sample of time-dependent nearest-neighbor conductances that are bounded but are permitted to vanish over time intervals of positive Lebesgue-length. Assuming only ergodicity of the…

Deterministic dynamical systems such as the baker maps are useful to shed light on some of the conditions verified by deterministic models in non-equilibrium statistical physics. We investigate a 2D dynamical system, enjoying a weak form of…

Dynamical systems can display a plethora of ergodic and ergodicity breaking behaviors, ranging from simple periodicity to ergodicity and chaos. Here we report an unusual type of non-ergodic behavior in a many-body discrete-time dynamical…

Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…

We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possible for the vertical translation flows on such flat…

A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…

In this paper, we investigate the ergodicity in total variation of the process $X_t$ related to some integro-differential operator with unbounded coefficients and describe the speed of convergence to the respective invariant measure. Some…

We provide a brief outlook on recent developments in regularity theory for nonuniformly elliptic problems, with special emphasis on those of variational nature.

We study various ergodic properties of C*-dynamical systems inspired by unique ergodicity. In particular we work in a framework allowing for ergodic properties defined relative to various subspaces, and in terms of weighted means. Our main…

We directly detect the ergodicity breaking in a lattice glass model by a numerical simulation. The obtained results nicely agree with those by the cavity method that the model on a regular random graph exhibits a dynamical transition with…

The potential applications of boundary functionals of random processes, such as the extreme values of these processes, the moment of first reaching a fixed level, the value of the process at the moment of reaching the level, the moment of…

Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…

We give a sufficient condition for the ergodicity of the Lebesgue measure for an iterated function system of diffeomorphisms. This is done via the induced iterated function system on the space of continuum (which is called hyper-space). We…

In this paper, we prove a uniform version of quantum unique ergodicity for high-frequency eigensections of a certain series of unitary flat bundles over arithmetic surfaces.

The Edwards hypothesis of ergodicity of blocked configurations for gently tapped granular materials is tested for abstract models of spin systems on random graphs and spin chains with kinetic constraints. The tapping dynamics is modeled by…

We propose an extension of ergodic theory which focuses on the identification of ergodicity in terms of the uniqueness of the invariant measure. We first explain the concept for the doubling maps, which can be analyzed using Fourier…

We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…