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Hyperbolic Lyapunov–Perron regular points and smooth invariant measures
Part of
- Dynamical systems with hyperbolic behavior
NAWAF ALANSARI
Journal:

Ergodic Theory and Dynamical Systems / Volume 43 / Issue 7 / July 2023

Published online by Cambridge University Press:

17 June 2022, pp. 2177-2200

Print publication:

July 2023
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For a $C^{1+\alpha }$ diffeomorphism f of a compact smooth manifold, we give a necessary and sufficient condition that guarantees that if the set of hyperbolic Lyapunov–Perron regular points has positive volume, then f preserves a smooth measure. We use recent results on symbolic coding of $\chi $ -non-uniformly hyperbolic sets and results concerning the existence of SRB measures for them.