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arXiv · 2401.02776

Finite Measures of Maximal Entropy for an Open Set of Partially Hyperbolic Diffeomorphisms

Juan Carlos Mongez·Maria Jose Pacifico
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Abstract

We consider partially hyperbolic diffeomorphisms $f$ with a one-dimensional central direction such that the unstable entropy exceeds the stable entropy. Our main result proves that such maps have a finite number of ergodic measures of maximal entropy. Moreover, any $C^{1+}$ diffeomorphism near $f$ in the $C^1$ topology possesses at most the same number of ergodic measures of maximal entropy. Our contribution is in extending the findings in [4] to arbitrary dimensions. We believe our technique, essentially distinct from the one in that paper, is robust and may find applications in further contexts.

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Juan Carlos Mongez, Maria Jose Pacifico. 2024-01-05. Finite Measures of Maximal Entropy for an Open Set of Partially Hyperbolic Diffeomorphisms. https://arxiv.org/abs/2401.02776

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