Continuity of Lyapunov Exponents for Cocycles with Invariant Holonomies

By Lucas Backes, Aaron W. Brown, C. Butler. 2015

57 citations recorded by the source corpus.

We prove a conjecture of Viana which states that Lyapunov exponents vary continuously when restricted to $GL(2,\mathbb{R})$-valued cocycles over a subshift of finite type which admit invariant holonomies that depend continuously on the cocycle.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/421c0a3c7985674abb63ff312d15778e70379463

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In Mathematical Physics

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Citations in the corpus

• Sharp Hölder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles (2017, background): “.d. random products of matrices in GL(d,R) was proved by Avila, Eskin, and Viana [7]. If the base dynamics is a subshift of finite type or, more generally, a hyperbolic set, then Backes, Brown, Butler [9] proved that Lyapunov exponents are always continuous among H¨older continuous fiber-bunched SL(2,”