Quasi-multiplicativity of typical cocycles

Abstract

We show that typical (in the sense of Bonatti-Viana) Hölder and fiber-bunched $G{L}_d(\mathbb{R})$-valued cocycles over a subshift of finite type are uniformly quasi-multiplicative with respect to all singular value potentials. We prove the continuity of the singular value pressure and its corresponding (necessarily unique) equilibrium state for such cocycles, and apply this result to repellers. Moreover, we show that the pointwise Lyapunov spectrum is closed and convex, and establish partial multifractal analysis on the level sets of pointwise Lyapunov exponents for such cocycles.

References in corpus (6)

• Lyapunov spectrum of asymptotically sub-additive potentials
• Equilibrium states of the pressure function for products of matrices
• Non-conformal repellers and the continuity of pressure for matrix cocycles
• The thermodynamic approach to multifractal analysis
• Continuity of Lyapunov Exponents for Cocycles with Invariant Holonomies
• Simplicity of Lyapunov spectrum for linear cocycles over non-uniformly hyperbolic systems

Cited by in corpus (3)

• The joint spectrum
• Entropy spectrum of Lyapunov exponents for typical cocycles
• Totally ergodic generalised matrix equilibrium states have the Bernoulli property