JournalscmhVol. 93, No. 2pp. 377–400

Strongly dissipative surface diffeomorphisms

  • Sylvain Crovisier

    Université Paris-Sud, Orsay, France
  • Enrique Pujals

    Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
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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 CC^\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).

Cite this article

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

DOI 10.4171/CMH/438