Continuity of Lyapunov exponents in the C0 topology

2016/12/30 by Viana, Marcelo, Yang, Jiagang
#37A99 #37C40 #37D20 #37H15 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.09361

Abstract

We prove that the Bochi-Mañé theorem is false, in general, for linear cocycles over non-invertible maps: there are C0-open subsets of linear cocycles that are not uniformly hyperbolic and yet have Lyapunov exponents bounded from zero.

Related

• Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents
• Hölder continuity of the Lyapunov exponents of linear cocycles over hyperbolic maps
• Continuity of Lyapunov exponents in all Hölder topologies for irreducible cocycles
• Monochromatic nonuniform hyperbolicity
• Discontinuity of Lyapunov exponents for SL(2,ℝ) valued cocycles