Robust vanishing of all Lyapunov exponents for iterated function systems

Jairo Bochi; Christian Bonatti; Lorenzo J. Díaz

doi:10.1007/s00209-013-1209-y

Robust vanishing of all Lyapunov exponents for iterated function systems

Jairo Bochi, Christian Bonatti, Lorenzo J. Díaz

Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	469-503
Number of pages	35
Journal	Mathematische Zeitschrift
Volume	276
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-013-1209-y
State	Published - Feb 2014

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "Robust vanishing of all Lyapunov exponents for iterated function systems",

abstract = "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.",

author = "Jairo Bochi and Christian Bonatti and D{\'i}az, {Lorenzo J.}",

note = "Funding Information: The authors received support from CNPq, FAPERJ, PRONEX (Brazil), Balzan–Palis Project, Brazil–France Cooperation Program in Mathematics, and ANR (France). ",

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AU - Bochi, Jairo

AU - Bonatti, Christian

AU - Díaz, Lorenzo J.

N1 - Funding Information: The authors received support from CNPq, FAPERJ, PRONEX (Brazil), Balzan–Palis Project, Brazil–France Cooperation Program in Mathematics, and ANR (France).

PY - 2014/2

Y1 - 2014/2

N2 - 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.

AB - 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.

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JO - Mathematische Zeitschrift

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ER -

Robust vanishing of all Lyapunov exponents for iterated function systems

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