相关论文: A characterization of physical measures for system…
For a partially hyperbolic attractor with a center bundle splitting in a dominatedway into one-dimensional subbundles we show that for Lebesgue almost every point there is anempirical measure from $x$ with a SRB component. Moreover if the…
Consider a topologically exact $C^3$ interval map without non-flat critical points. Following the works we did in \cite{LiRiv12two}, we give two equivalent characterizations of hyperbolic H\"{o}lder continuous potential in terms of the…
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…
We consider the set of partially hyperbolic symplectic diffeomorphisms which are accessible, have 2-dimensional center bundle and satisfy some pinching and bunching conditions. In this set, we prove that the non-uniformly hyperbolic maps…
We show that for any $C^1$ partially hyperbolic diffeomorphism, there is a full volume subset, such that any Cesaro limit of any point in this subset satisfies the Pesin formula for partial entropy. This result has several important…
We describe some recent results on the dynamics of singular-hyperbolic (or Lorenz-like) attractors: attractors in this class are expansive and so sensitive with respect to initial data; they admit a unique physical measure whose support is…
In hyperbolic dynamics, a well-known result is: every hyperbolic Lyapunov stable set, is attracting; it's natural to wonder if this result is maintained in the sectional-hyperbolic dynamics. This question is still open, although some…
We prove that the statistical properties of random perturbations of a nonuniformly hyperbolic diffeomorphism are described by a finite number of stationary measures. We also give necessary and sufficient conditions for the stochastic…
The paper deals with topical issues of modern mathematical theory of dynamical chaos and its applications. At present, it is customary to assume that dynamical chaos in finitedimensional smooth systems can exist in three different forms.…
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…
For a class of partially hyperbolic $C^k$, $k>1$ diffeomorphisms with circle center leaves we prove existence and finiteness of physical (or Sinai-Ruelle-Bowen) measures, whose basins cover a full Lebesgue measure subset of the ambient…
In this paper we revisit uniformly hyperbolic basic sets and the domination of Oseledets splittings at periodic points. We prove that periodic points with simple Lyapunov spectrum are dense in non-trivial basic pieces of Cr-residual…
"Sticky" motion in mixed phase space of conservative systems is difficult to detect and to characterize, in particular for high dimensional phase spaces. Its effect on quasi-regular motion is quantified here with four different measures,…
We describe a method, using periodic points and determinants, for giving alternative expressions for dynamical quantities (including Lyapunov exponents and Hausdorff dimension of invariant sets) associated to analytic hyperbolic systems.…
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 establish the existence and finiteness of equilibrium states for a class of partially hyperbolic endomorphisms. In our first result, we assume that the central direction is simple. In the second result, we consider the case where there…
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.…
We prove for $C^\infty$ non-singular flows on three-dimensional compact manifolds with positive entropy, there are at most finitely many ergodic measures of maximal entropy. This result extends the notable work of Buzzi-Crovisier-Sarig…
For dynamical systems satisfying the approximate $\mathbb{Z}^{d}$ or $\mathbb{Z}_+^{d}$-product property and asymptotically entropy expansiveness, we establish a precise description of the structure of their space of invariant measures. In…
We obtain the following dichotomy for accessible partially hyperbolic diffeomorphisms of 3-dimensional manifolds having compact center leaves: either there is a unique entropy maximizing measure, this measure has the Bernoulli property and…