A generic C1 map has no absolutely continuous invariant probability measure

Artur Avila, Jairo Bochi

Research output: Contribution to journalReview articlepeer-review

13 Scopus citations


Let M be a smooth compact manifold of any dimension. We consider the set of C1 maps f:M → M which have no absolutely continuous (with respect to Lebesgue) invariant probability measure. We show that this is a residual set in the C1 topology.

Original languageEnglish (US)
Article number011
Issue number11
StatePublished - Nov 1 2006

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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