相关论文: Physical measures for infinite-modal maps

We prove that for certain actions of a discrete countable residually finite amenable group acting on a compact metric space with specification property, periodic measures are dense in the set of invariant measures.

We study optimal solutions to an abstract optimization problem for measures, which is a generalization of classical variational problems in information theory and statistical physics. In the classical problems, information and relative…

We define a notion of entropy for an infinite family $\mathcal{C}$ of measurable sets in a probability space. We show that the mean ergodic theorem holds uniformly for $\mathcal{C}$ under every ergodic transformation if and only if…

We describe a construction process of a relevant measure in any non-empty compact metric space. This probability measure has invariance properties with respect to isometric maps defined on open sets. These properties imply that this measure…

In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be…

We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation…

We investigate mixing properties of piecewise affine non-Markovian maps acting on $[0,1]^2$ or $[0,1]^3$ and preserving the Lebesgue measure, which are natural generalizations of the {\it heterochaos baker maps} introduced in [Y. Saiki, H.…

We consider the problem of when a symbolic dynamical system supports a Borel probability measure that is invariant under every element of its automorphism group. It follows readily from a classical result of Parry that the full shift on…

We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…

We consider the dynamics of strongly dissipative H\'enon-like maps in the plane, around the first bifurcation parameter $a^*$ at which the uniform hyperbolicity is destroyed by the formation of homoclinic or heteroclinic tangencies inside…

This work gives a computable formula for the average measure theoretic entropy of a family of expanding on average random Blaschke products, generalizing work by Pujals, Roberts and Shub [Expanding maps of the circle revisited: positive…

We consider the ergodic theory of plane rational maps that preserve the natural holomorphic volume form on the algebraic torus. Specifically we construct natural invariant probability measures for a large class of such maps by intersecting…

We study the measure theoretic properties of typical C 0 maps of the interval. We prove that any ergodic measure is pseudo-physical, and conversely, any pseudo-physical measure is in the closure of the ergodic measures, as well as in the…

We study collections of point masses which move freely along the real line and stick together when they collide via perfectly inelastic collisions. We quantify the way particles stick together and explain how to associate a probability…

One of the goals of this article is to define a an unified setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure. We first remark that some…

We construct SRB measures for endomorphisms satisfying conditions far weaker than the non-uniformly expansion. As a consequence, the definition of non-uniformly expanding map can be weakened. We also prove the existence of an absolutely…

Let $M$ be a compact $n$-dimensional Riemanian manifold, End($M$) the set of the endomorphisms of $M$ with the usual $\mathcal{C}^0$ topology and $\phi: M\to\mathbb{R}$ continuous. We prove that there exists a dense subset of $\mathcal{A}$…

We study the sigma-finite measures in the space of vector-valued distributions on the manifold $X$ with Laplace transform $$\Psi(f)=\exp\{-\theta\int_X\ln||f(x)||dx\}, \theta>0.$$ We also consider the weak limit of Haar measures on the…

Three equivalent characterizations of probability measures through independence criteria are given. These characterizations lead to a family of Brascamp--Lieb-type inequalities for relative entropy, determine equilibrium states and sharp…

We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we explicitly describe all ergodic probability measures invariant with respect to the tail equivalence relation (or the…