Related papers: Measure-expansive systems

Given a piecewise $C^{1+\beta}$ map of the interval, possibly with critical points and discontinuities, we construct a symbolic model for invariant probability measures with nonuniform expansion that do not approach the critical points and…

In this paper we prove a recent conjecture by M. Hirsch, which says that if $(f,\Omega)$ is a discrete time monotone dynamical system, with $f\colon \Omega\to\Omega$ a homeomorphism on an open connected subset of a finite dimensional vector…

Motivated by Sarnak's conjecture on M\"obius orthogonality, we investigate the general problem of orthogonality for a bounded sequence to topological models of characteristic classes of measure-preserving automorphisms. Our main observation…

We establish the existence and fundamental properties of the equilibrium measure in uniformly quasiregular dynamics. We show that a uniformly quasiregular endomorphism $f$ of degree at least 2 on a closed Riemannian manifold admits an…

We consider random perturbations of non-uniformly expanding maps, possibly having a non-degenerate critical set. We prove that, if the Lebesgue measure of the set of points failing the non-uniform expansion or the slow recurrence to the…

We develope a new and general notion of parametric measure models and statistical models on an arbitrary sample space $\Omega$ which does not assume that all measures of the model have the same null sets. This is given by a diffferentiable…

For dynamical systems with the shadowing property, we provide a method of approximation of invariant measures by ergodic measures supported on odometers and their almost 1-1 extensions. For a topologically transitive system with the…

Let $\mathcal{E}$ denote the space of entire functions with the topology of uniform convergence on compact sets. The action of $\mathbb C$ by translations on $\mathcal E$ is defined by $T_zf(w) = f(w+z)$. Let $\mathcal{U}$ denote the set of…

Let f be a polynomial or a rational function which has r summable critical points. We prove that there exists an r-dimensional manifold in an appropriate space containing f such that for every smooth curve in it through f, the ratio between…

We consider the open set constructed by M. Shub in [42] of partially hyperbolic skew products on the space $\mathbb{T}^2\times \mathbb{T}^2$ whose non-wandering set is not stable. We show that there exists an open set $\mathcal{U}$ of such…

We study stable conditional measures for a certain equilibrium measure for hyperbolic endomorphisms, on basic sets with overlaps; we show that these conditional measures are geometric probabilities and measures of maximal stable dimension.…

The aim of this note is to introduce a notion of dynamical entropy, which we call infinite-product entropy, for probability measures on (countable) infinite cartesian product of any measurable space with itself. The idea behind the…

We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…

In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, $T$, in a product space whose alphabet is a perfect and separable metric space (thus,…

Let $f : [0, 1] \to [0, 1]$ be a piecewise expanding unimodal map of class $C^{k+1}$, with $k \geq 1$, and $\mu = \rho dx$ the (unique) SRB measure associated to it. We study the regularity of $\rho$. In particular, points $\mathcal{N}$…

It is known that piecewise affine surface homeomorphisms always have measures of maximal entropy. This is easily seen to fail in the discontinuous case. Here we describe a piecewise affine, globally continuous surface map with no measure of…

We prove the equivalence between geometric and analytic definitions of quasiconformality for a homeomorphism $f\colon X\rightarrow Y$ between arbitrary locally finite separable metric measure spaces, assuming no metric hypotheses on either…

In this article we introduce and study a natural form of expansivity, that we call \textit{metric-independent expansiveness}, for group actions on metrizable spaces. This notion means \textit{expansive with respect to every compatible…

Let $f$ be a $C^{1+bv}$ circle diffeomorphism with irrational rotation number. As established by Douady and Yoccoz in the eighties, for any given $s>0$ there exists a unique automorphic measure of exponent $s$ for $f$. In the present paper…

In this paper, we extend a Ma\~n\'e's famous result on expansive homeomorphisms, originally presented in [17], to the setting of flows. Specifically, we provide a complete characterization of minimal expansive flows without fixed points on…