Related papers: Lyapunov exponents for expansive homeomorphisms

Let $M$ be a 2$d-$dimensional compact connected Riemannian manifold and $\omega$ be a symplectic form on $M$. In this paper, we prove that a symplectic diffeomorphism, with all Lyapunov exponent zero for almost everywhere, can be $C^1$…

The article states that for every compact manifold M of dimension 4 or higher there is an area U in a set of smooth diffeomorphisms over M such that every map f from U has local maximal partially hyperbolic attractor and nonatomic ergodic…

We give a new definition for a Lyapunov exponent (called new Lyapunov exponent) associated to a continuous map. Our first result states that these new exponents coincide with the usual Lyapunov exponents if the map is differentiable. Then,…

For $m$ given square matrices $A_0, A_1, \cdots, A_{m-1}$ ($m\ge 2$), one of which is assumed to be of rank $1$, and for a given sequence $(\omega_n)$ in $\{0,1, \cdots, m-1\}^\mathbb{N}$, the following limit, if it exists,…

In this paper we investigate the relation between measure expansiveness and hyperbolicity. We prove that non atomic invariant ergodic measures with all of its Lyapunov exponents positive is positively measure-expansive. We also prove that…

We consider compact invariant sets \Lambda for C^{1} maps in arbitrary dimension. We prove that if \Lambda contains no critical points then there exists an invariant probability measure with a Lyapunov exponent \lambda which is the minimum…

In this paper, we study two properties of the Lyapunov exponents under small perturbations: one is when we can remove zero Lyapunov exponents and the other is when we can distinguish all the Lyapunov exponents. The first result shows that…

We show that for any C^1+alpha diffeomorphism of a compact Riemannian manifold, every non-atomic, ergodic, invariant probability measure with non-zero Lyapunov exponents is approximated by uniformly hyperbolic sets in the sense that there…

This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques…

We consider hyperbolic and partially hyperbolic diffeomorphisms on compact manifolds. Associated with invariant foliation of these systems, we define some topological invariants and show certain relationships between these topological…

We consider a large class of 2D area-preserving diffeomorphisms that are not uniformly hyperbolic but have strong hyperbolicity properties on large regions of their phase spaces. A prime example is the Standard map. Lower bounds for…

We introduce and study the Lyapunov numbers -- quantitative measures of the sensitivity of a dynamical system $(X,f)$ given by a compact metric space $X$ and a continuous map $f:X \to X$. In particular, we prove that for a minimal…

In this paper we study the relationship between Lyapunov exponents and the induced map on cohomology for $C^{1}-$diffeomorphisms on compact manifolds. We show that if the induced map on cohomology has spectral radius strictly larger than 1,…

In this paper we introduce a notion of expansiveness for a set valued map defined on a topological space different from that given by Richard Williams at \cite{Wi, Wi2} and prove that the topological entropy of an expansive set valued map…

We consider a smooth expanding map g on the circle of degree 2. It is known that the Lyapunov exponent of g with respect to the unique invariant measure that is absolutely continuous with respect to the Lebesgue measure is positive and less…

Let $K$ be an algebraically closed and complete nonarchimedean field with characteristic $0$ and let $f\in K[z]$ be a polynomial of degree $d\ge 2$. We study the Lyapunov exponent $L(f,\mu)$ of $f$ with respect to an $f$-invariant and…

Let f be a dominating meromorphic self-map of a compact Kahler manifold. We give an inequality for the Lyapounov exponents of some ergodic measures of f using the metric entropy and the dynamical degrees of f. We deduce the hyperbolicity of…

We consider linear cocycles over non-uniformly hyperbolic dynamical systems. The base system is a diffeomorphism $f$ of a compact manifold $X$ preserving a hyperbolic ergodic probability measure $\mu$. The cocycle $A$ over $f$ is Holder…

We present a new method for the computation of Lyapunov exponents utilizing representations of orthogonal matrices applied to decompositions of M or MM_trans where M is the tangent map. This method uses a minimal set of variables, does not…

We prove two inequalities between the Lyapunov exponents of a diffeomorphism and its local recurrence properties. We give examples showing that each of the inequalities is optimal.