Non-hyperbolic ergodic measures with large support

Abstract

We prove that there is a residual subset $\mathcal{S}$ in ${\text{Diff}}^1(M)$ such that, for every $f\in \mathcal{S}$, any homoclinic class of $f$ with invariant one dimensional central bundle containing saddles of different indices (i.e. with different dimensions of the stable invariant manifold) coincides with the support of some invariant ergodic non-hyperbolic (one of the Lyapunov exponents is equal to zero) measure of $f$.

References in corpus (2)

• Symbolic extensions for partially hyperbolic diffeomorphisms
• Nonhyperbolicity of invariant measures on maximal attractor

Cited by in corpus (12)

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• Periodic measures and partially hyperbolic homoclinic classes
• Variational principle for nonhyperbolic ergodic measures: Skew products and elliptic cocycles
• On the existence of non-hyperbolic ergodic measures as the limit of periodic measures
• Non-hyperbolic ergodic measures and horseshoes in partially hyperbolic homoclinic classes
• Path connectedness and entropy density of the space of ergodic hyperbolic measures
• Center Lyapunov exponents in partially hyperbolic dynamics
• Circle diffeomorphisms forced by expanding circle maps
• Ergodic measures with multi-zero Lyapunov exponents inside homoclinic classes
• Porcupine-like horseshoes: Transitivity, Lyapunov spectrum, and phase transitions