Related papers: Ergodic Average Of Typical Orbits And Typical Func…
We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…
We study the limiting behavior of multiple ergodic averages involving several not necessarily commuting measure preserving transformations. We work on two types of averages, one that uses iterates along combinatorial parallelepipeds, and…
In this paper, we show that for several interesting systems beyond uniform hyperbolicity, any generic continuous function has a unique maximizing measure with zero entropy. In some cases, we also know that the maximizing measure has full…
We derive the first two moments of generic positive stochastic functionals in terms of the one- and two-time probability density functions of the underlying random walk, and we prove ergodicity of observables in stationary random walks.…
Time averages extracted from single-particle trajectories in complex media often vary strongly from one trajectory to another, even for long measurement times. Such persistent trajectory-to trajectory scatter is commonly observed in…
Let $K$ be the Cantor set. We prove that arbitrarily close to a homeomorphism $T:K\rightarrow K$ there exists a homeomorphism $\widetilde T:K\rightarrow K$ such that the $\alpha$-limit and the $\omega$-limit of every orbit is a periodic…
We find a normal form which describes the high energy dynamics of a class of piecewise smooth Fermi-Ulam ping pong models; depending on the value of a single real parameter, the dynamics can be either hyperbolic or elliptic. In the first…
We provide examples of transitive partially hyperbolic dynamics (specific but paradigmatic examples of homoclinic classes) which blend different types of hyperbolicity in the one-dimensional center direction. These homoclinic classes have…
We consider the unit speed parametrization of the horocycle flow on infinite Abelian covers of compact surfaces of negative curvature. We prove an asymptotic result for the ergodic integrals of sufficiently regular functions. In the case of…
We prove a general result about the decomposition on ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of ergodic components with the boundary of the orbit tree…
We show that an $R^d$-topological dynamical system equipped with an invariant ergodic measure has discrete spectrum if and only it is $\mu$-mean equicontinuous (proven for $Z^d$ before). In order to do this we introduce mean equicontinuity…
This article is devoted to the study of the historic set of ergodic averages in some nonuniformly hyperbolic systems. In particular, our results hold for the robust classes of multidimensional nonuniformly expanding local diffeomorphisms…
We study mean convergence of multiple ergodic averages, where the iterates arise from smooth functions of polynomial growth that belong to a Hardy field. Our results include all logarithmico-exponential functions of polynomial growth, such…
Consider a topological dynamical system where the group is abelian and the topologies are locally compact and second-countable. Given an invariant measure for this system, we show that if its dynamical spectrum is contained in some Borel…
Autonomous robotic exploration in remote and extreme environments allows scientists to model complex transport phenomena and collective behaviors described by continuously deforming flow fields. Although these environments are naturally…
We explore the properties of test-particle orbits in "bumpy" spacetimes - stationary, reflection-symmetric, asymptotically flat solutions of Einstein equations that have a non-Kerr (anomalous) higher-order multipole-moment structure but can…
Using an asymptotically additive sequence of continuous functions as a restrictive condition, this paper studies the relations of several ergodic averages for asymptotically additive potentials. Basic properties of conditional maximum…
In the present paper, we study the distribution of the return points in the fibers for a RDS (random dynamical systems) nonuniformly expanding preserving an ergodic probability, we also show the abundance of nonlacunarity of hyperbolic…
In this article we prove that for a $C^{1+\alpha}$ diffeomorphism on a compact Riemannian manifold, if there is a hyperbolic ergodic measure whose support is not uniformly hyperbolic, then the topological entropy of the set of irregular…
In this article, we study the behaviour of discrete one-dimensional dynamical systems associated to functions on finite sets. We formalise the global orbit pattern formed by all the periodic orbits (gop) as the ordered set of periods when…