Lucas Backes

Continuity of Lyapunov exponents for cocycles with invariant holonomies

We prove a conjecture of Viana which states that Lyapunov exponents vary continuously when restricted to

Rigidity of fiber bunched cocycles

GL(2,\mathbb{R})

Continuity of Lyapunov exponents is equivalent to continuity of Oseledets subspaces

-valued cocycles over a subshift of finite type which admit invariant holonomies that depend continuously on the cocycle.

On the periodic approximation of Lyapunov exponents for semi-invertible cocycles

We prove a rigidity theorem for fiber bunched matrix-valued Hölder cocycles over hyperbolic homeomorphisms. More precisely, we show that two such cocycles are cohomologous if and only if they have conjugated periodic data.

A Livšic Theorem for Matrix Cocycles Over Non-uniformly Hyperbolic Systems

We prove that, for semi-invertible continuous cocycles, continuity of Lyapunov exponents is equivalent to continuity, in measure, of Oseledets subspaces.

A Remark on the Invertibility of Semi-invertible Cocycles

We prove that, for semi-invertible linear cocycles, Lyapunov exponents of ergodic measures may be approximated by Lyapunov exponents on periodic points.

Periodic approximation of Oseledets subspaces for semi-invertible cocycles

We prove a Livšic-type theorem for Hölder continuous and matrix-valued cocycles over non-uniformly hyperbolic systems. More precisely, we prove that whenever

Simplicity of Lyapunov spectrum for linear cocycles over non-uniformly hyperbolic systems

(f,\mu )