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Mathematische Zeitschrift

, Volume 276, Issue 1–2, pp 469–503 | Cite as

Robust vanishing of all Lyapunov exponents for iterated function systems

  • Jairo Bochi
  • Christian Bonatti
  • Lorenzo J. Díaz
Article

Abstract

Given any compact connected manifold \(M\), we describe \(C^2\)-open sets of iterated functions systems (IFS’s) admitting fully-supported ergodic measures whose Lyapunov exponents along \(M\) are all zero. Moreover, these measures are approximated by measures supported on periodic orbits. We also describe \(C^1\)-open sets of IFS’s admitting ergodic measures of positive entropy whose Lyapunov exponents along \(M\) are all zero. The proofs involve the construction of non-hyperbolic measures for the induced IFS’s on the flag manifold.

Notes

Acknowledgments

We are grateful to the referee for some corrections.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jairo Bochi
    • 1
  • Christian Bonatti
    • 2
  • Lorenzo J. Díaz
    • 1
  1. 1.Departamento de MatemáticaPontifícia Universidade Católica do Rio de JaneiroRio de JaneiroBrazil
  2. 2.Institut de Mathématiques de BourgogneDijonFrance

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