相关论文: Negative Lyapunov exponent of circle maps forced b…

In this work we treat a famous topic in Ergodic Theory and Dynamical Systems: uniformly expanding maps. We relate regularity of expanding maps and conjugacies with Lyapunov exponents, metric and topological entropies for expanding maps of…

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…

We prove that for any holomorphic map, and any bounded orbit which does not accumulate to a singular set or to an attracting cycle, its lower Lyapunov exponent is non-negative. The same result holds for unbounded orbits, for maps with a…

For a smooth expanding circle map, we show that the empirical distribution of Lyapunov exponents of periodic points of any fixed period is close to normal, with an error that decreases as the period grows. This establishes a version of the…

In this paper we study the Lyapunov spectrum rigidity for random walks of expanding maps on unit circle $\mathbb{S}^1$ and Anosov diffeomorphisms on $d$-torus $\mathbb{T}^d$. Let $\nu$ be a probability supported on the set of expanding maps…

In the present work we obtain rigidity results analysing the set of regular points, in the sense of Oseledec's Theorem. It is presented a study on the possibility of an Anosov diffeomorphisms having all Lyapunov exponents defined…

We prove that for Anosov maps of the $3$-torus if the Lyapunov exponents of absolutely continuous measures in every direction are equal to the geometric growth of the invariant foliations then $f$ is $C^1$ conjugated to his linear part.

We show the existence of large $\mathcal C^1$ open sets of area preserving endomorphisms of the two-torus which have no dominated splitting and are non-uniformly hyperbolic, meaning that Lebesgue almost every point has a positive and a…

We show that $C(X)$ admits an equivalent pointwise lower semicontinuous locally uniformly rotund norm provided $X$ is Fedorchuk compact of spectral height 3. In other words $X$ admits a fully closed map $f$ onto a metric compact $Y$ such…

We consider the topological behaviors of continuous maps with one topological attractor on compact metric space $X$. This kind of map is a generalization of maps such as topologically expansive Lorenz map, unimodal map without homtervals…

For any integer $r$ with $1\leq r<\infty$, we present a one-parameter family $F_\sigma$ $(0<\sigma<1)$ of 2-dimensional piecewise $\mathcal C^r$ expanding maps such that each $F_\sigma$ has an observable (i.e. Lebesgue positive) Lyapunov…

We consider products of a i.i.d. sequence in a set $\{f_1,\ldots,f_m\}$ of preserving orientation diffeomorphisms of the circle. we can naturally associate a Lyapunov exponent $\lambda$. Under few assumptions, it is known that $\lambda\leq…

We prove that there exists an open and dense subset $\mathcal{U}$ in the space of $C^{2}$ expanding self-maps of the circle $\mathbb{T}$ such that the Lyapunov minimizing measures of any $T\in{\mathcal U}$ are uniquely supported on a…

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,…

We show that for a large class of potential functions and big coupling constant $\lambda$ the Schr\"odinger cocycle over the expanding map $x\mapsto bx ~( \text{mod} 1)$ on $\mathbb{T}$ has a Lyapunov exponent $>(\log\lambda)/4$ for all…

We analyze the two-point motions of iterated function systems on the unit interval generated by expanding and contracting affine maps, where the expansion and contraction rates are determined by a pair $(M,N)$ of integers. This dynamics…

We show how the existence of three objects, $\Omega_{\rm trap}$, ${\bf W}$, and $C$, for a continuous piecewise-linear map $f$ on $\mathbb{R}^N$, implies that $f$ has a topological attractor with a positive Lyapunov exponent. First,…

Let (M,d) be a compact metric space and f:M --> M an expansive homeomorphism. We define Lyapunov exponents L(f,m)_{max} and l(f,mu)_{min} for an f-invariant measure m. When L(f,m)_{max} > 0 and l(f,mu)_{min} < 0 can be interpreted as a weak…

For a non-generic, yet dense subset of $C^1$ expanding Markov maps of the interval we prove the existence of uncountably many Lyapunov optimizing measures which are ergodic, fully supported and have positive entropy. These measures are…

We show that the continuity property of Lyapunov exponents proved in \cite{BCS-Exponents} for smooth surface diffeomorphisms extends to smooth interval maps, in the case when the map only has non-flat critical points and the entropies…