Related papers: Intrinsic ergodicity for certain nonhyperbolic rob…
We study the amount of nonhyperbolicity within a broad class of (nonhyperbolic) partially hyperbolic diffeomorphisms with a one-dimensional center. For that, we focus on the center Lyapunov exponent and the entropy of its level sets. We…
In this paper, we consider certain partially hyperbolic diffeomorphisms with center of arbitrary dimension and obtain continuity properties of the topological entropy under $C^1$ perturbations. The systems considered have subexponential…
We prove that for a wide family of non-uniformly hyperbolic maps and hyperbolic potentials we have equilibrium stability, i.e. the equilibrium states depend continuously on the dynamics and the potential. For this we deduce that the…
This article is devoted to the investigation of the topological pressure of generic points for nonuniformly hyperbolic systems via Pesin theory. In particular, our result can be applied to the nonuniformly hyperbolic diffeomorphisms…
In this paper, we study ergodic optimization of continuous functions for flows by concentrating on the entropy spectrum of their maximizing measures. Precisely, over a wide family of flows with non-uniformly hyperbolic structure, we obtain…
This article is devoted to study which conditions imply that a topological dynamical system is mean sensitive and which do not. Among other things we show that every uniquely ergodic, mixing system with positive entropy is mean sensitive.…
We study transitive step skew-product maps modeled over a complete shift of $k$, $k\ge2$, symbols whose fiber maps are defined on the circle and have intermingled contracting and expanding regions. These dynamics are genuinely nonhyperbolic…
We prove existence of maximal entropy measures for an open set of non-uniformly expanding local diffeomorphisms on a compact Riemannian manifold. In this context the topological entropy coincides with the logarithm of the degree, and these…
It is shown that if a non-invertible area preserving local homeomorphism on $\mathbb{T}^2$ is homotopic to a linear expanding or hyperbolic endomorphism, then it must be topologically transitive. This gives a complete characterization, in…
We endow the set of all invariant measures of a topological dynamical system with a metric $\bar{\rho}$, which induces a topology stronger than the the weak$^*$-topology. Then, we study the closedness of ergodic measures within a…
We consider Hamiltonian diffeomorphisms of the Euclidean space, generated by compactly supported time-dependent perturbations of hyperbolic quadratic forms. We prove that, under some natural assumptions, such a diffeomorphism must have…
We prove results related to robust transitivity and density of periodic points of Partially Hyperbolic Diffeomorphisms under conditions involving Accessibility and a property in the tangent bundle .
Previous work introduced two measure-conjugacy invariants: the $f$-invariant (for actions of free groups) and $\Sigma$-entropy (for actions of sofic groups). The purpose of this paper is to show that the $f$-invariant is a special case of…
In this paper, we pay attention to a weaker version of Walters's question on the existence of non-uniform cocycles for uniquely ergodic minimal dynamical systems on non-degenerate connected spaces. We will classify such dynamical systems…
We study a class of asymptotically entropy-expansive $C^1$ diffeomorphisms with dominated splitting on a compact manifold $M$, that satisfy the specification property. This class includes, in particular, transitive Anosov diffeomorphisms…
We prove existence of equilibrium states with special properties for a class of distance expanding local homeomorphisms on compact metric spaces and continuous potentials. Moreover, we formulate a C$^1$ generalization of Pesin's Entropy…
We prove existence of finitely many ergodic equilibrium states for a large class of non-uniformly expanding local homeomorphisms on compact manifolds and Holder continuous potentials with not very large oscillation. No Markov structure is…
Previously, Reynolds showed that any irreducible nonsurjective endomorphism can be represented by an irreducible immersion on a finite graph. We give a new proof of this and also show a partial converse holds when the immersion has…
We discuss recent progress in understanding the dynamical properties of partially hyperbolic diffeomorphisms that preserve volume. The main topics addressed are density of stable ergodicity and stable accessibility, center Lyapunov…
We discuss the Sinai method of proving ergodicity of a discontinuous Hamiltonian system with (non-uniform) hyperbolic behavior.