On the density of hyperbolicity and homoclinic bifurcations for 3D-diffeomorphisms in attracting regions

DOI10.3934/DCDS.2006.16.179zbMath1111.37008OpenAlexW2079277084MaRDI QIDQ862088

Enrique R. Pujals

Publication date: 5 February 2007

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2006.16.179

zbMATH Keywords

nonhyperbolicityPalis conjecture

Mathematics Subject Classification ID

Generic properties, structural stability of dynamical systems (37C20) Dynamical systems with hyperbolic orbits and sets (37D05) Partially hyperbolic systems and dominated splittings (37D30) Bifurcations connected with nontransversal intersection in dynamical systems (37G25) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (7)

A $C^2$ generic trichotomy for diffeomorphisms: Hyperbolicity or zero Lyapunov exponents or the $C^1$ creation of homoclinic bifurcations ⋮ Partial hyperbolicity far from homoclinic bifurcations ⋮ Birth of homoclinic intersections: a model for the central dynamics of partially hyperbolic systems ⋮ CENTER MANIFOLDS FOR PARTIALLY HYPERBOLIC SETS WITHOUT STRONG UNSTABLE CONNECTIONS ⋮ Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms ⋮ An extension of the ergodic closing lemma ⋮ Hölder stability for \(C^r\) central translations

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