5 papers
The fibered rotation number
Pedro Duarte, Anton Gorodetski, Victor Kleptsyn
We provide an explicit formula for an increment of the fibered rotation number of a one-parameter family of circle cocycles over any ergodic transformation in terms of invariant me…
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…
Obstructions to the regularity of the Lyapunov exponents for non-compact random Schrödinger cocycles
Pedro Duarte, Tomé Graxinha, Tomé Graxinha
In this paper, we present a class of random Schrödinger cocycles showing that, for random cocycles with non-compact support, the presence of certain finite moment conditions is ess…
Hölder continuity of Lyapunov exponents for non-invertible and non-compact random cocycles
Pedro Duarte, Tomé Graxinha
We study the regularity of Lyapunov exponents for random linear cocycles taking values in $\Mat_m(\R)$ and driven by i.i.d. processes. Under three natural conditions - finite expon…
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 o…