Robust vanishing of all Lyapunov exponents for iterated function systems

Jairo Bochi, Christian Bonatti, Lorenzo J. Díaz

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Given any compact connected manifold M, we describe C2-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 C1-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.

Original languageEnglish (US)
Pages (from-to)469-503
Number of pages35
JournalMathematische Zeitschrift
Issue number1-2
StatePublished - Feb 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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