35 citations · 120 across the 19 of their papers we have counts for
23 papers
Random 2D linear cocycles II: statistical properties
Pedro Duarte, Marcelo Durães, Tomé Graxinha +1
Consider the space of two dimensional random linear cocycles over a shift in finitely many symbols, with at least one singular and one invertible matrix. We provide an explicit for…
Random 2D linear cocycles I: dichotomic behavior
Pedro Duarte, Marcelo Durães, Tomé Graxinha +1
In this paper we establish a Bochi-Mañé type dichotomy in the space of two dimensional, nonnegative determinant matrix valued, locally constant linear cocycles over a Bernoulli or…
Hölder continuity of the Lyapunov exponent for Markov cocycles via Furstenberg's Formula
Ao Cai, Marcelo Durães, Silvius Klein +1
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 maxima…
Statistical properties for mixing Markov chains with applications to dynamical systems
Ao Cai, Pedro Duarte, Silvius Klein
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 estimate…
A dynamical Thouless formula
Jamerson Bezerra, Ao Cai, Pedro Duarte +2
In this paper we establish an abstract, dynamical Thouless-type formula for affine families of cocycles. This result extends the classical formula rela…
Furstenberg Theory of Mixed Random-Quasiperiodic Cocycles
Ao Cai, Pedro Duarte, Silvius Klein
We derive a criterion for the positivity of the maximal Lyapunov exponent of generic mixed random-quasiperiodic linear cocycles, a model introduced in a previous work. This result…