Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows.

DOI10.1016/S0294-1449(03)00016-7zbMath1045.37006OpenAlexW1985639436MaRDI QIDQ1406889

Federico Rodriguez Hertz, Aubin Arroyo

Publication date: 7 September 2003

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2003__20_5_805_0

zbMATH Keywords

dominated splittinghomoclinic tangency\(C^1\)-topologyuniformly hyperbolicsingular cyclethree-dimensional manifoldPoincaré flow\(C^1\)-vector field

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Generic properties, structural stability of dynamical systems (37C20) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Partially hyperbolic systems and dominated splittings (37D30) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

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