Internal perturbations of homoclinic classes: non-domination, cycles, and self-replication

DOI10.1017/S0143385712000028zbMath1303.37008arXiv1011.2935MaRDI QIDQ4928748

Nicolas Gourmelon, Sylvain Crovisier, Christian Bonatti, Lorenzo J. Dıaz

Publication date: 18 June 2013

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.2935

zbMATH Keywords

homoclinic tangencyheterodimensional cycleadapted perturbationlack of dominated splittingsectional dissipativityviral homoclinic classes

Mathematics Subject Classification ID

Generic properties, structural stability of dynamical systems (37C20) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (12)

Robust criterion for the existence of nonhyperbolic ergodic measures ⋮ Hyperbolicity versus weak periodic orbits inside homoclinic classes ⋮ Flexible periodic points ⋮ Homoclinic tangencies leading to robust heterodimensional cycles ⋮ On bi-Lyapunov stable homoclinic classes ⋮ Ergodic measures with multi-zero Lyapunov exponents inside homoclinic classes ⋮ Local perturbations of conservativeC¹diffeomorphisms ⋮ Partial hyperbolicity and homoclinic tangencies ⋮ Historic behavior in nonhyperbolic homoclinic classes ⋮ A Franks’ lemma that preserves invariant manifolds ⋮ Hyperbolicity versus non-hyperbolic ergodic measures inside homoclinic classes ⋮ Nontransverse heterodimensional cycles: Stabilisation and robust tangencies

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