arXiv subjects

Aline Melo

Publications and source records attributed to Aline Melo.

3 recordsLinked to original sources

arXiv2025

Analyticity of the Lyapunov exponents of random products of matrices

This paper is concerned with the study of random (Bernoulli and Markovian) product of matrices on a compact space of symbols. We establish the analyticity of the maximal Lyapunov exponent as a function of the transition probabilities, thus extending the results and methods of Y. Peres from a finite to an infinite (but compact) space of symbols. Our approach combines the spectral properties of the associated Markov operator with the theory of holomorphic functions in Banach spaces.

math.DS↗

arXiv2022

Hölder continuity of the Lyapunov exponent for Markov cocycles via Furstenberg's Formula

This paper is concerned with the study of linear cocycles over uniformly ergodic Markov shifts on a compact space of symbols. We establish the joint Hölder continuity of the maximal Lyapunov exponent as a function of the cocycle and the transition kernel in the vicinity of any irreducible cocycle with simple maximal Lyapunov exponent. Our approach, via Furstenberg's formula, shows the Hölder continuous dependence on the data of the stationary measure of the projective cocycle and in particular provides a more computable Hölder exponent.

math.DS↗

arXiv2019

Uniform convergence rate for Birkhoff means of certain uniquely ergodic toral maps

We obtain estimates on the uniform convergence rate of the Birkhoff average of a continuous observable over torus translations and affine skew product toral transformations. The convergence rate depends explicitly on the modulus of continuity of the observable and on the arithmetic properties of the frequency defining the transformation. Furthermore, we show that for the one dimensional torus translation, these estimates are nearly optimal.

math.DS↗