Related papers: On Anosov diffeomorphisms with asymptotically conf…
In this paper we introduce a new methodology for smooth rigidity of Anosov diffeomorphisms based on "matching functions." The main observation is that under certain bunching assumptions on the diffeomorphism the periodic cycle functionals…
In this paper we obtain local rigidity results for linear Anosov diffeomorphisms in terms of Lyapunov exponents. More specifically, we show that given an irreducible linear hyperbolic automorphism $L$ with simple real eigenvalues with…
We consider two transitive $3$-dimensional Anosov flows which do not preserve volume and which are continuously conjugate to each other. Then, disregarding certain exceptional cases, such as flows with $C^1$ regular stable or unstable…
We prove transitivity for volume preserving $C^{1+}$ diffeomorphisms on $\mathbb{T}^3$ which are isotopic to a linear Anosov automorphism along a path of weakly partially hyperbolic diffeomorphisms.
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…
Despite the invertible setting, Anosov endomorphisms may have infinitely many unstable directions. Here we prove, under transitivity assumption, that an Anosov endomorphism on a closed manifold $M,$ is either special (that is, every $x \in…
We obtain smooth conjugacy between non-necessarily special Anosov endomorphisms in the conservative case. Among other results, we prove that a strongly special $C^{\infty}-$Anosov endomorphism of $\mathbb{T}^2$ and its linearization are…
In this work we lead with expanding maps of the circle and Anosov diffeomorphisms on $\mathbb{T}^d, d \geq 2.$ We prove that, for these maps, \textit{constant periodic data} imply \textit{same periodic data of these maps and their…
We found a dichotomy involving the unstable Lyapunov exponent of a special Anosov endomorphism of the torus induced by the conjugacy with the linearization. In fact, either every unstable leaf meets on a set of zero measure the set for…
We consider a smooth area-preserving Anosov diffeomorphism $f\colon \mathbb T^2\rightarrow \mathbb T^2$ homotopic to an Anosov automorphism $L$ of $\mathbb T^2$. It is known that the positive Lyapunov exponent of $f$ with respect to the…
We study the effects that the constant periodic data condition have on topological entropy of Anosov diffeomorphisms. Under constant periodic data condition we prove that Anosov diffeomorphism has finitely many measures of maximal entropy…
It is known that transitive Anosov diffeomorphisms have a unique measure of maximal entropy (MME). Here we discuss the converse question. Under suitable hypothesis on Lyapunov exponents on the set of periodic points and the structure of the…
Given a $C^0$ conjugacy between two Anosov diffeomorphisms, the matching periodic data problem asks whether this conjugacy is smooth provided spectral data of the diffeomorphisms match at periodic points. We show that if the two $C^0$…
We prove that every $C^2$ Anosov diffeomorphism in a compact and connected Riemannian manifold has a unique SRB and physical probability measure, whose basin of attraction covers Lebesgue almost every point in the manifold. Then, we use…
We prove the transitivity of real Anosov diffeomorphisms, which are Anosov diffeomorphisms where stable and unstable spaces decompose into a continuous sum of invariant one-dimensional sub-spaces with uniform contraction/expansion over the…
Weprovethattheasymptoticsofergodicintegralsalonganinvariant foliation of a toral Anosov diffeomorphism, or of a pseudo-Anosov diffeomorphism on a compact orientable surface of higher genus, are determined (up to a logarithmic error) by the…
In this paper, we focus on the rigidity of $C^{2+}$-smooth codimension-one stable foliations of Anosov diffeomorphisms. Specifically, we show that if the regularity of these foliations is slightly bigger than $2$, then they will have the…
We study the existence of Anosov diffeomorphisms on complete open surfaces. We show that under the assumptions of density of periodic points and uniform geometry that such diffeomorphisms have a system of Margulis measures, which are a…
This work is addressed to study Anosov endomorphisms of $\mathbb{T}^d,$ $d\geq 3.$ We are interested to obtain metric and topological information on such Anosov endomorphism by comparison between their Lyapunov exponents and the ones of its…
We classify quasiconformal Anosov flows whose strong stable and unstable distributions are at least two dimensional and the sum of these two distributions is smooth. We deduce from this classification result the complete classification of…