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partial hyperbolic diffeomorphisms

Ergodic Theory and Dynamical Systems (1)

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$C^{1}$-openness of non-uniform hyperbolic diffeomorphisms with bounded $C^{2}$-norm
Part of
- Dynamical systems with hyperbolic behavior
CHAO LIANG, KARINA MARIN, JIAGANG YANG
Journal:

Ergodic Theory and Dynamical Systems / Volume 40 / Issue 11 / November 2020

Published online by Cambridge University Press:

06 June 2019, pp. 3078-3104

Print publication:

November 2020
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We study the $C^{1}$-topological properties of the subset of non-uniform hyperbolic diffeomorphisms in a certain class of $C^{2}$ partially hyperbolic symplectic systems which have bounded $C^{2}$ distance to the identity. In this set, we prove the stability of non-uniform hyperbolicity as a function of the diffeomorphism and the measure, and the existence of an open and dense subset of continuity points for the center Lyapunov exponents. These results are generalized to the volume-preserving context.