Robust vanishing of all Lyapunov exponents for iterated function systems
Dynamical Systems
2013-06-05 v2
Abstract
Given any compact connected manifold , we describe -open sets of iterated functions systems (IFS's) admitting fully-supported ergodic measures whose Lyapunov exponents along are all zero. Moreover, these measures are approximated by measures supported on periodic orbits. We also describe -open sets of IFS's admitting ergodic measures of positive entropy whose Lyapunov exponents along are all zero. The proofs involve the construction of non-hyperbolic measures for the induced IFS's on the flag manifold.
Cite
@article{arxiv.1211.3435,
title = {Robust vanishing of all Lyapunov exponents for iterated function systems},
author = {Jairo Bochi and Christian Bonatti and Lorenzo J. Díaz},
journal= {arXiv preprint arXiv:1211.3435},
year = {2013}
}
Comments
Minor corrections were made. This is the final version, to appear in Mathematische Zeitschrift