Abundance of elliptic dynamics on conservative three-flows

DOI10.1080/14689360802162872zbMath1158.37010OpenAlexW2075340419MaRDI QIDQ3548763

Mário Bessa, Pedro Duarte

Publication date: 17 December 2008

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689360802162872

zbMATH Keywords

hyperbolic setsdominated splittingvolume-preserving flows

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Periodic orbits of vector fields and flows (37C27) Generic properties, structural stability of dynamical systems (37C20) Partially hyperbolic systems and dominated splittings (37D30)

Related Items (9)

Dynamics of conservative Bykov cycles: tangencies, generalized Cocoon bifurcations and elliptic solutions ⋮ A dichotomy in area-preserving reversible maps ⋮ Generic Hamiltonian Dynamical Systems: An Overview ⋮ Area-Preserving Diffeomorphisms from theC 1Standpoint ⋮ On \(C^1\)-generic chaotic systems in three-manifolds ⋮ Hamiltonian elliptic dynamics on symplectic $4$-manifolds ⋮ Conservative flows with various types of shadowing ⋮ Homoclinic tangencies versus uniform hyperbolicity for conservative 3-flows ⋮ Contributions to the geometric and ergodic theory of conservative flows

Cites Work

• The Lyapunov exponents of generic volume-preserving and symplectic maps
• Partial hyperbolicity for symplectic diffeomorphisms
• Dynamics of generic 2-dimensional linear differential systems
• Hyperbolic invariant sets with positive measures
• A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources
• Partial hyperbolicity and robust transitivity
• An ergodic closing lemma
• The C¹ Closing Lemma, including Hamiltonians
• Partial hyperbolicity or dense elliptic periodic points for 𝐶¹-generic symplectic diffeomorphisms
• Regularisation C∞ des champs vectoriels qui préservent l'élément de volume
• Quasi-Elliptic Periodic Points in Conservative Dynamical Systems
• The generic symplectic C^{1}-diffeomorphisms of four-dimensional symplectic manifolds are hyperbolic, partially hyperbolic or have a completely elliptic periodic point
• Genericity of zero Lyapunov exponents
• A pasting lemma and some applications for conservative systems
• The Lyapunov exponents of generic zero divergence three-dimensional vector fields
• Projective hyperbolicity and fixed points
• Generic Properties of Conservative Systems

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