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Statistical stability for robust classes of maps with non-uniform expansion

  • JOSÉ F. ALVES (a1) and MARCELO VIANA (a2)
  • DOI: http://dx.doi.org/10.1017/S0143385702000019
  • Published online: 01 January 2002
Abstract

We consider open sets of transformations in a manifold M, exhibiting non-uniformly expanding behavior in some forward invariant domain U\subset M. Assuming that each transformation has a unique Sinai–Ruelle–Bowen (SRB) measure in U, and some general uniformity conditions, we prove that the SRB measure varies continuously with the dynamics in the L1-norm. We also describe a concrete application.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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