Dimensional entropies and semi-uniform hyperbolicity
Jerome Buzzi (LM-Orsay)
TL;DR
This paper explores dimensional entropies, introduces entropy-hyperbolicity for diffeomorphisms, and provides new properties, proofs, and conditions, advancing the understanding of entropy-related dynamical systems.
Contribution
It introduces a new notion of entropy-hyperbolicity and offers new conditions and proofs related to dimensional entropies in dynamical systems.
Findings
Defined entropy-expanding maps
Introduced entropy-hyperbolicity for diffeomorphisms
Provided new sufficient conditions for these properties
Abstract
We describe dimensional entropies introduced in a previous work list some of their properties and give some new proofs. These entropies allowed the definition of entropy-expanding maps. We introduce a new notion of entropy-hyperbolicity for diffeomorphisms. We indicate some simple sufficient conditions (some of them new) for these properties. We conclude by some work in progress and more questions.
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