arXiv subjects

Adriana Sánchez

Publications and source records attributed to Adriana Sánchez.

5 recordsLinked to original sources

arXiv2026

Hölder regularity of the top Lyapunov exponent for random matrix products with low-dimensional equator

We investigate the regularity of Lyapunov exponents for products of random invertible matrices of arbitrary dimension $d\ge 2$. We prove that the top Lyapunov exponent is pointwise Hölder continuous with respect to the Wasserstein-Hausdorff distance in the space of probability measures with compact support, in the case where this exponent is simple and the equator has dimension equal to or less than one.

math.DS↗

arXiv2021

Analyticity of the Lyapunov exponents of random products of quasi-periodic cocycles

We show that the top Lyapunov exponent $λ_+(p)$ , $p = (p_1, \cdots, p_N)$ with $p_i >0$ for each $i$, associated with a random product of quasi-periodic cocycles depends real analytically on the transition probabilities $p$ whenever $λ_+(p)$ is simple. Moreover if the spectrum at $p$ is simple (all Lyapunov exponents having multiplicity one ) then all Lyapunov exponents depend real analytically on $p$.

math.DS↗

arXiv2020

Equilibrium states for maps isotopic to Anosov

In this work we address the problem of existence and uniqueness (finiteness) of ergodic equilibrium states for partially hyperbolic diffeomorphisms isotopic to Anosov on $\mathbb{T}^4$, with 2-dimensional center foliation. To do so we propose to study the disintegration of measures along 1-dimensional subfoliations of the center bundle. Moreover, we obtain a more general result characterizing the disintegration of ergodic measures in our context.

math.DS↗

arXiv2020

Lyapunov exponents of probability distributions with non-compact support

We prove that the Lyapunov exponents, cosidered as functions of measures with non compact support, are semicontinuous with respect to the Wasserstein topology but not with respect to the weak* topology. Moreover, we prove that they are not continuous in the Wasserstein topology.

math.DS↗

arXiv2017

The set of fiber-bunched cocycles with nonvanishing Lyapunov exponents over a partially hyperbolic map is open

We prove that the set of fiber-bunched $SL(2,\mathbb{R})$-valued Hölder cocycles with nonvanishing Lyapunov exponents over a volume preserving, accessible and center-bunched partially hyperbolic diffeomorphism is open. Moreover, we present an example showing that this is no longer true if we do not assume acessibility in the base dynamics.

math.DS↗