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 Henon 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.

Sylvain Crovisier

Enrique Pujals

Charles Tresser

Acta Mathematica

发表所有数学领域最高质量的原创研究论文。

The journal Acta Mathematica is dedicated to publishing original research papers of the highest quality across all areas of mathematics.

《Acta Mathematica》期刊致力于发表所有数学领域内最高质量的原创研究论文。

Category	Quartile
数学	1
数学, 数学	1

Mildly dissipative diffeomorphisms of the disk with zero entropy

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Mildly dissipative diffeomorphisms&nbsp;of the disk with zero entropy

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Mildly dissipative diffeomorphisms of the disk with zero entropy