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arXiv · 2005.14278

Mildly dissipative diffeomorphisms of the disk with zero entropy

Sylvain Crovisier·Enrique Pujals·Charles Tresser
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Abstract

We discuss the dynamics of smooth diffeomorphisms of the disc with vanishing topological entropy which satisfy the mild dissipation property introduced in [CP]. In particular it contains the H\'enon maps with Jacobian up to 1/4. We prove that these systems are either (generalized) Morse Smale or infinitely renormalizable. In particular we prove for this class of diffeomorphisms a conjecture of Tresser: any diffeomorphism in the interface between the sets of systems with zero and positive entropy admits doubling cascades. This generalizes for these surface dynamics a well known consequence of Sharkovskii's theorem for interval maps.

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Sylvain Crovisier, Enrique Pujals, Charles Tresser. 2020-05-28. Mildly dissipative diffeomorphisms of the disk with zero entropy. https://arxiv.org/abs/2005.14278

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