Homoclinic tangencies versus uniform hyperbolicity for conservative 3-flows

DOI10.1016/J.JDE.2009.07.020zbMath1189.37021OpenAlexW2052697722WikidataQ125377731 ScholiaQ125377731MaRDI QIDQ1039755

Jorge Rocha, Mário Bessa

Publication date: 23 November 2009

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

Full work available at URL: https://doi.org/10.1016/j.jde.2009.07.020

zbMATH Keywords

Anosov flowsthree-dimensional flowvolume-preserving flowhomoclinic tangencies

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Dynamics induced by flows and semiflows (37C10) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (8)

Dynamics of conservative Bykov cycles: tangencies, generalized Cocoon bifurcations and elliptic solutions ⋮ Stability properties of divergence-free vector fields ⋮ Topological stability for conservative systems ⋮ Volume-preserving diffeomorphisms with the \(\mathcal{M}_0\)-shadowing properties ⋮ Stable weakly shadowable volume-preserving systems are volume-hyperbolic ⋮ Conservative flows with various types of shadowing ⋮ Unnamed Item ⋮ Hamiltonian suspension of perturbed Poincaré sections and an application

Cites Work

• Unnamed Item
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• Dominated splitting and zero volume for incompressible three flows
• Abundance of elliptic dynamics on conservative three-flows
• Regularisation C∞ des champs vectoriels qui préservent l'élément de volume
• Quasi-Elliptic Periodic Points in Conservative Dynamical Systems
• Abundance of elliptic isles at conservative bifurcations
• A pasting lemma and some applications for conservative systems
• Open questions leading to a global perspective in dynamics
• On the Volume Elements on a Manifold

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