Collision, explosion and collapse of homoclinic classes

DOI10.1088/0951-7715/17/3/013zbMath1046.37035arXiv1205.1023OpenAlexW2128202221MaRDI QIDQ4812576

Bianca Santoro, Lorenzo J. Dıaz

Publication date: 23 August 2004

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.1023

zbMATH Keywords

saddle-node bifurcationshomoclinic classesgeneric \(C^1\)-diffeomorphismsmaximal transitive sets

Mathematics Subject Classification ID

Generic properties, structural stability of dynamical systems (37C20) Partially hyperbolic systems and dominated splittings (37D30) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Infinite nonwandering sets arising in bifurcations of dynamical systems (37G30) Bifurcations connected with nontransversal intersection in dynamical systems (37G25)

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Skew product cycles with rich dynamics: From totally non-hyperbolic dynamics to fully prevalent hyperbolicity ⋮ Mingled hyperbolicities: ergodic properties and bifurcation phenomena (an approach using concavity) ⋮ Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes ⋮ Measures of maximal entropy for surface diffeomorphisms ⋮ ON THE <i>F</i>-EXPANDING OF HOMOCLINIC CLASSES

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