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arXiv · 1211.3435

Robust vanishing of all Lyapunov exponents for iterated function systems

Jairo Bochi·Christian Bonatti·Lorenzo J. Díaz
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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.

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Jairo Bochi, Christian Bonatti, Lorenzo J. Díaz. 2013-06-04. Robust vanishing of all Lyapunov exponents for iterated function systems. https://arxiv.org/abs/1211.3435

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