Robust vanishing of all Lyapunov exponents for iterated function systems
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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.
We are grateful to the referee for some corrections.
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