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Hölder continuity of the Lyapunov exponents of linear cocycles over hyperbolic maps
Pedro Duarte, Silvius Klein, Mauricio Poletti
Given a hyperbolic homeomorphism on a compact metric space, consider the space of linear cocycles over this base dynamics which are Hölder continuous and whose projective actions a…
Random product of quasi-periodic cocycles
Jamerson Bezerra, Mauricio Poletti
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 ,…
On the genericity of positive exponents of conservative skew products with two-dimensional fibers
Davi Obata, Mauricio Poletti
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 f…
A Livšic theorem for matrix cocycles over non-uniformly hyperbolic systems
Lucas Backes, Mauricio Poletti
We prove a Livšic-type theorem for Hölder continuous and matrix-valued cocycles over non-uniformly hyperbolic systems. More precisely, we prove that whenever is a non-unifo…