On invariant holonomies between centers

Abstract

We prove that for $C^{1+\theta }$, $\theta$-bunched, dynamically coherent partially hyperbolic diffeomorphisms, the stable and unstable holonomies between center leaves are $C^1$ and the derivative depends continuously on the points and on the map. Also for $C^{1+\theta }$, $\theta$-bunched partially hyperbolic diffeomorphism, the derivative cocycle restricted to the center bundle has invariant continuous holonomies which depend continuously on the map. This generalizes previous results by Pugh-Shub-Wilkinson, Burns-Wilkinson, Brown, Obata, Avila-Santamaria-Viana, Marin.

References in corpus (4)

• Lyapunov exponents of partially hyperbolic volume-preserving maps with 2-dimensional center bundle
• $C^r$-density of (non-uniform) hyperbolicity in partially hyperbolic symplectic diffeomorphisms
• $C^1$-openness of non-uniform hyperbolic diffeomorphisms with bounded $C^2$ norm
• Accessibility for dynamically coherent partially hyperbolic diffeomorphisms with 2D center