Related papers: Ergodic Optimization of Super-continuous Functions…

For a class of piecewise hyperbolic maps in two dimensions, we propose a combinatorial definition of topological entropy by counting the maximal, open, connected components of the phase space on which iterates of the map are smooth. We…

We present a concise, but systematic, review of the ergodicity issue in strongly correlated systems. After giving a brief historical overview, we analyze the issue within the Green's function formalism by means of the equations of motion…

In robotics, ergodic control extends the tracking principle by specifying a probability distribution over an area to cover instead of a trajectory to track. The original problem is formulated as a spectral multiscale coverage problem,…

We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such measures that converge to a zero-entropy measure.

Using a simple, annealed model, some of the key features of the recently introduced extremal optimization heuristic are demonstrated. In particular, it is shown that the dynamics of local search possesses a generic critical point under the…

We prove the existence of a successful coupling for $n$ particles in the symmetric inclusion process. As a consequence we characterize the ergodic measures with finite moments, and obtain sufficient conditions for a measure to converge in…

This paper addresses structures of state space in quasiperiodically forced dynamical systems. We develop a theory of ergodic partition of state space in a class of measure-preserving and dissipative flows, which is a natural extension of…

We generalize stochastic subgradient descent methods to situations in which we do not receive independent samples from the distribution over which we optimize, but instead receive samples that are coupled over time. We show that as long as…

We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…

A subshift with linear block complexity has at most countably many ergodic measures, and we continue of the study of the relation between such complexity and the invariant measures. By constructing minimal subshifts whose block complexity…

The purpose of this paper is to study the time average behavior of Markov chains with transition probabilities being kernels of completely continuous operators, and therefore to provide a sufficient condition for a class of Markov chains…

This paper investigates performance guarantees on coverage-based ergodic exploration methods in environments containing disturbances. Ergodic exploration methods generate trajectories for autonomous robots such that time spent in each area…

We introduce the concept of a heterodimensional cycle of hyperbolic ergodic measures and a special type of them that we call rich. Within a partially hyperbolic context, we prove that if two measures are related by a rich heterodimensional…

The ergodic decomposition theorem is a cornerstone result of dynamical systems and ergodic theory. It states that every invariant measure on a dynamical system is a mixture of ergodic ones. Here we formulate and prove the theorem in terms…

We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…

We construct analytic pseudo-rotations on the sphere and the disk with specific properties. We obtain analytic pseudo-rotations which are ergodic. Then, in opposition to ergodicity, we construct analytic pseudo-rotations which exhibit a…

We form a sequence of oblong matrices by evaluating an integrable vector-valued function along the orbit of an ergodic dynamical system. We obtain an almost sure asymptotic result for the permanents of those matrices. We also give an…

In this paper we study the dynamics and ergodic theory of certain economic models which are implicitly defined. We consider 1-dimensional and 2-dimensional overlapping generations models, a cash-in-advance model, heterogeneous markets and a…

An ergodic support $X_0$ of a dynamical system $(X,T)$ with metrizable compact phase space $X$ is the set of all points $x\in X$ such that the corresponding sequence of empirical measures $\delta_{x,n} = (\delta_x +\delta_{Tx}+\dots…

In the simplest sequential decision problem for an ergodic stochastic process X, at each time n a decision u_n is made as a function of past observations X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is known that…