Lyapunov exponents of partially hyperbolic volume-preserving maps with 2-dimensional center bundle

Abstract

We consider the set of partially hyperbolic symplectic diffeomorphisms which are accessible, have 2-dimensional center bundle and satisfy some pinching and bunching conditions. In this set, we prove that the non-uniformly hyperbolic maps are $C^r$ open and there exists a $C^r$ open and dense subset of continuity points for the center Lyapunov exponents. We also generalize these results to volume-preserving systems.

Final version. Published online on Annales de l'Institut Henri Poincaré, Analyse non linéaire

References in corpus (1)

• $C^r$-density of (non-uniform) hyperbolicity in partially hyperbolic symplectic diffeomorphisms

Cited by in corpus (4)

• Unstable entropy in smooth ergodic theory
• $C^1$-openness of non-uniform hyperbolic diffeomorphisms with bounded $C^2$ norm
• Non-uniformly hyperbolic endomorphisms
• On invariant holonomies between centers