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pro vyhledávání: '"Poletti, Mauricio"'
For $C^{1+}$ maps, possibly non-invertible and with singularities, we prove that each homoclinic class of an adapted hyperbolic measure carries at most one adapted hyperbolic measure of maximal entropy. We then apply this to study the finiteness/uniq
Externí odkaz:
http://arxiv.org/abs/2405.04676
Autor:
Lima, Yuri, Poletti, Mauricio
Given a $C^{1+\beta}$ flow $\varphi$ with positive speed on a closed smooth Riemannian manifold, we code two homoclinically related $\varphi$-invariant probabilities by an irreducible countable topological Markov flow. As an application, we give proo
Externí odkaz:
http://arxiv.org/abs/2403.03759
Autor:
Bezerra, Jamerson, Poletti, Mauricio
The purpose of these notes is to discuss the advances in the theory of Lyapunov exponents of linear $\text{SL}_2(\mathbb{R})$ cocycles over hyperbolic maps. The main focus is around results regarding the positivity of the Lyapunov exponent and the re
Externí odkaz:
http://arxiv.org/abs/2306.03470
Autor:
Crovisier, Sylvain, Poletti, Mauricio
We prove a generalization of a so called "invariance principle" for partially hyperbolic diffeomorphisms: if an invariant probability measure has all its center Lyapunov exponents equal to zero then the measure admits a center disintegration that is
Externí odkaz:
http://arxiv.org/abs/2210.14989
We study the $u$-Gibbs measures of a certain class of uniformly hyperbolic skew products on $\mathbb{T}^4$. These systems have a strong unstable and a weak unstable directions. We show that $C^r$-dense and $C^2$-open in this set every $u$-Gibbs measu
Externí odkaz:
http://arxiv.org/abs/2209.09151
Given a hyperbolic homeomorphism on a compact metric space, consider the space of linear cocycles over this base dynamics which are H\"older continuous and whose projective actions are partially hyperbolic dynamical systems. We prove that locally nea
Externí odkaz:
http://arxiv.org/abs/2110.10265
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 flows in
Externí odkaz:
http://arxiv.org/abs/2010.11808
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Autor:
Bezerra, Jamerson, Poletti, Mauricio
Given a finite set of quasi-periodic cocycles the random product of them is defined as the random composition according to some probability measure. We prove that the set of $C^r$, $0\leq r \leq \infty$ (or analytic) $k+1$-tuples of quasi periodic co
Externí odkaz:
http://arxiv.org/abs/1907.00815
Autor:
Obata, Davi, Poletti, Mauricio
In this paper we study the existence of positive Lyapunov exponents for three different types of skew products, whose fibers are compact Riemannian surfaces and the action on the fibers are by volume preserving diffeomorphisms. These three types incl
Externí odkaz:
http://arxiv.org/abs/1809.03874