Commentarii Mathematici Helvetici

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Volume 93, Issue 2, 2018, pp. 377–400
DOI: 10.4171/CMH/438

Published online: 2018-05-31

Strongly dissipative surface diffeomorphisms

Sylvain Crovisier[1] and Enrique Pujals[2]

(1) Université Paris-Sud, Orsay, France
(2) Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil

We introduce a class of volume-contracting surface diffeomorphisms whose dynamics is intermediate between one-dimensional dynamics and general surface dynamics. For that type of systems one can associate to the dynamics a reduced one-dimensional model and it is proved a type of $C^\infty$-closing lemma on the support of every ergodic measure. We also show that this class contains Hénon maps with Jacobian in (–1/4, 1/4).

Keywords: Surface diffeomorphisms, attractors, closing lemma, stable manifold

Crovisier Sylvain, Pujals Enrique: Strongly dissipative surface diffeomorphisms. Comment. Math. Helv. 93 (2018), 377-400. doi: 10.4171/CMH/438