Fragile cycles

DOI10.1016/J.JDE.2011.12.002zbMath1279.37022arXiv1103.3255OpenAlexW4206157003MaRDI QIDQ765939

Christian Bonatti, Lorenzo J. Dıaz

Publication date: 22 March 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.3255

zbMATH Keywords

homoclinic classhyperbolic setchain recurrence class\(C^1\)-robustnessheterodimensional class

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Partially hyperbolic systems and dominated splittings (37D30) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (3)

Tame dynamics and robust transitivity chain-recurrence classes versus homoclinic classes ⋮ Hénon-Like Families and Blender-Horseshoes at Nontransverse Heterodimensional Cycles ⋮ On super-exponential divergence of periodic points for partially hyperbolic systems

Cites Work

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• There are no \(C^{1}\)-stable intersections of regular Cantor sets
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• Stabilization of heterodimensional cycles
• SURVEY Towards a global view of dynamical systems, for the C¹-topology
• Equilibrium states for partially hyperbolic horseshoes
• Porcupine-like horseshoes: Transitivity, Lyapunov spectrum, and phase transitions
• Periodic points and homoclinic classes
• ROBUST HETERODIMENSIONAL CYCLES AND $C^1$-GENERIC DYNAMICS
• Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes
• Generic robustness of spectral decompositions
• Hyperbolic Limit Sets
• Recurrence and genericity

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