Related papers: Statistical properties of generalized-Viana maps

The standard map, paradigmatic conservative system in the $(x,p)$ phase space, has been recently shown to exhibit interesting statistical behaviors directly related to the value of the standard map parameter $K$. A detailed numerical…

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…

We consider skew-product maps over circle rotations $x\mapsto x+\alpha$ (mod 1) with factors that take values in SL(2,R). This includes maps of almost Mathieu type. In numerical experiments, with $\alpha$ the inverse golden mean, Fibonacci…

In this article we will describe a new construction for Gibbs measures for hyperbolic attractors generalizing the original construction of Sinai, Bowen and Ruelle of SRB measures. The classical construction of the SRB measure is based on…

We consider the period-doubling and intermittency transitions in iterated nonlinear one-dimensional maps to corroborate unambiguously the validity of Tsallis' non-extensive statistics at these critical points. We study the map…

Let $T$ be an expanding Markov map with a countable number of inverse branches and a repeller $\Lambda$ contained within the unit interval. Given $\alpha \in \R_+$ we consider the set of points $x \in \Lambda$ for which $T^n(x)$ hits a…

In this note we construct measures of maximal entropy for a certain class of maps with critical points called Viana maps. The main ingredients of the proof are the non-uniform expansion features and the slow recurrence (to the critical set)…

We study the local dynamics of generic skew-products tangent to the identity, i.e. maps of the form $P(z,w)=(p(z), q(z,w))$ with $dP_0=\mathrm{id}$. More precisely, we focus on maps with non-degenerate second differential at the origin;…

In the present paper we focus on the problem of the existence of strange pseudohyperbolic attractors for three-dimensional diffeomorphisms. Such attractors are genuine strange attractors in that sense that each orbit in the attractor has a…

We study multiscale integrator numerical schemes for a class of stiff stochastic differential equations (SDEs). We consider multiscale SDEs with potentially multiple attractors that behave as diffusions on graphs as the stiffness parameter…

We investigate dynamical systems obtained by coupling two maps, one of which is chaotic and is exemplified by an Anosov diffeomorphism, and the other is of gradient type and is exemplified by a N-pole-to-S-pole map of the circle. Leveraging…

We consider strange attractors of two dimensional generalized map with one nonlinearity such that Lozi, H\'{e}non and Belykh maps are particular cases of it. We describe technique of invariant expanding and contracting cones creation for…

We construct countable Markov partitions for non-uniformly hyperbolic diffeomorphisms on compact manifolds of any dimension, extending earlier work of O. Sarig for surfaces. These partitions allow us to obtain symbolic coding on invariant…

In a context of non-uniformly expanding maps, possibly with the presence of a critical set, we prove the existence of finitely many ergodic equilibrium states for hyperbolic potentials. Moreover, the equilibrium states are expanding…

We introduce the Markov extension, represented schematically as a tower, to the study of dynamical systems with holes. For tower maps with small holes, we prove the existence of conditionally invariant probability measures which are…

For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here ``eigenvalue''…

We generalize the concept of convective (or velocity-dependent) Lyapunov exponent $\Lambda(v)$ to an entire spectrum $\Lambda(v,n)$. Our results are supported by the consistency between the outcome of the chronotopic approach [{\it S. Lepri…

We study hyperbolic skew products and the disintegration of the SRB measure into measures supported on local stable manifolds. Such a disintegration gives a method for passing from an observable $v$ on the skew product to an observable…

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 study a class of stochastic models of mass transport on discrete vertex set $V$. For these models, a one-parameter family of homogeneous product measures $\otimes_{i\in V} \nu_\theta$ is reversible. We prove that the set of mixtures of…