Historic behavior in non-hyperbolic homoclinic classes

Abstract

We show that $C^1$-generically for diffeomorphisms of manifolds of dimension $d\ge 3$, a homoclinic class containing saddles of different indices has a residual subset where the orbit of any point has historic behavior.

arXiv commentVersion 3 is accepted in Proceedings of the American Mathematical Society

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Cited by in corpus (8)

• Emergence via non-existence of averages
• Historic wandering domains near cycles
• Highly irregular orbits for subshifts of finite type: large intersections and emergence
• Lyapunov exponents for random maps
• Historic and physical wandering domains for wild blender-horseshoes
• Topological entropy and Hausdorff dimension of irregular sets for non-hyperbolic dynamical systems
• Ergodic Formalism for topological Attractors and historic behavior
• Sensitivity and historic behavior for continuous maps on Baire metric spaces