Related papers: Statistical properties of generalized-Viana maps
We extend the classical Lyapunov inequality on the measurable space with infinite measure and on the so-called Grand Lebesgue spaces (GLS). We find also the exact value for correspondent constant. Possible applications: Functional Analysis…
We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under very general conditions on the interval maps and perturbation types, we prove strong stochastic…
We study the topological dynamics of H\'enon maps. For a parameter set generalizing the Benedicks-Carleson parameters (the Wang-Young parameter set) we obtain the following: The pruning front conjecture (due to Cvitanovi\'c); A kneading…
We are concerned with hypersurfaces of $\mathbb{R}^N$ with constant nonlocal (or fractional) mean curvature. This is the equation associated to critical points of the fractional perimeter under a volume constraint. Our results are twofold.…
We study multifractal decompositions based on Birkhoff averages for sequences of functions belonging to certain classes of symbolically continuous functions. We do this for an expanding interval map with countably many branches, which we…
In this paper we obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced by the mild solutions of a family of scalar linear-dissipative parabolic problems over a minimal and uniquely ergodic…
We investigate the statistical properties of a piecewise smooth dynamical system by studying directly the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional…
We study the $L^q$-spectrum of measures in the plane generated by certain nonlinear maps. In particular we consider attractors of iterated function systems consisting of maps whose components are $C^{1+\alpha}$ and for which the Jacobian is…
We use the concept of Baire Ergodicity and Ergodic Formalism introduced to study topological and statistical attractors for interval maps, even with discontinuities. For that we also analyze the {\em wandering intervals attractors}. As a…
We study how physical measures vary with the underlying dynamics in the open class of $C^r$, $r>1$, strong partially hyperbolic diffeomorphisms for which the central Lyapunov exponents of every Gibbs $u$-state is positive. If transitive,…
We show that a sectional-hyperbolic attracting set for a H\"older-$C^1$ vector field admits finitely many physical/SRB measures whose ergodic basins cover Lebesgue almost all points of the basin of topological attraction. In addition, these…
For piecewise $C^1$ interval maps possibly containing critical points and discontinuities with negative Schwarzian derivative, under two summability conditions on the growth of the derivative and recurrence along critical orbits, we prove…
In this paper, we discuss a simple model for a field driven, thermostated random walk that is constructed by a suitable generalization of a multi-baker map. The map is a usual multi-baker, but perturbed by a thermostated external field that…
In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…
For a large class of transitive non-hyperbolic systems, we construct nonhyperbolic ergodic measures with entropy arbitrarily close to its maximal possible value. The systems we consider are partially hyperbolic with one-dimension central…
In this work, linearized multivariate skew polynomials over division rings are introduced. Such polynomials are right linear over the corresponding centralizer and generalize linearized polynomial rings over finite fields, group rings or…
We prove that, under a mild summability condition on the growth of the derivative on critical orbits any piecewise monotone interval map possibly containing discontinuities and singularities with infinite derivative (cusp map) admits an…
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product…
We study transitive step skew-product maps modeled over a complete shift of $k$, $k\ge2$, symbols whose fiber maps are defined on the circle and have intermingled contracting and expanding regions. These dynamics are genuinely nonhyperbolic…
We construct Markov partitions for non-invertible and/or singular nonuniformly hyperbolic systems defined on higher dimensional Riemannian manifolds. The generality of the setup covers classical examples not treated so far, such as geodesic…