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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 -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).
Cite this article
Sylvain Crovisier, Enrique Pujals, Strongly dissipative surface diffeomorphisms. Comment. Math. Helv. 93 (2018), no. 2, pp. 377–400