On \(C^1\)-robust transitivity of volume-preserving flows

DOI10.1016/J.JDE.2008.02.045zbMath1166.37002arXiv0707.2554OpenAlexW2963328181MaRDI QIDQ959852

Jorge Rocha, Mário Bessa

Publication date: 12 December 2008

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

Full work available at URL: https://arxiv.org/abs/0707.2554

zbMATH Keywords

ergodicityweak hyperbolicityvolume-preserving flowPoincaré flowrobustly transitive vector field

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Partially hyperbolic systems and dominated splittings (37D30) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (23)

Orbital shadowing property for generic divergence-free vector fields ⋮ Stability properties of divergence-free vector fields ⋮ A Franks' lemma for convex planar billiards ⋮ Generic Hamiltonian Dynamical Systems: An Overview ⋮ Divergence-free vector fields with orbital shadowing ⋮ Divergence-free vector fields with inverse shadowing ⋮ Vector fields with the asymptotic orbital pseudo-orbit tracing property ⋮ Billiards in generic convex bodies have positive topological entropy ⋮ Topological stability for conservative systems ⋮ The specification property for flows from the robust and generic viewpoint ⋮ Hyperbolicity and types of shadowing for \(C^1\) generic vector fields ⋮ Volume-preserving diffeomorphisms with the \(\mathcal{M}_0\)-shadowing properties ⋮ A new proof of Franks' lemma for geodesic flows ⋮ Realization of tangent perturbations in discrete and continuous time conservative systems ⋮ Stable weakly shadowable volume-preserving systems are volume-hyperbolic ⋮ Continuum-wise expansiveness for non-conservative or conservative systems ⋮ A generic incompressible flow is topological mixing ⋮ Conservative flows with various types of shadowing ⋮ Expansiveness and hyperbolicity in convex billiards ⋮ Homoclinic tangencies versus uniform hyperbolicity for conservative 3-flows ⋮ Unnamed Item ⋮ Hyperbolicity in the volume-preserving scenario ⋮ Contributions to the geometric and ergodic theory of conservative flows

Cites Work

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• The C¹ Closing Lemma, including Hamiltonians
• Perturbations of the derivative along periodic orbits
• Removing zero Lyapunov exponents in volume-preserving flows
• Regularisation C∞ des champs vectoriels qui préservent l'élément de volume
• Removing zero Lyapunov exponents
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• Projective hyperbolicity and fixed points
• Dynamics of Generic Multidimensional Linear Differential Systems
• On the Volume Elements on a Manifold
• Necessary Conditions for Stability of Diffeomorphisms
• Recurrence and genericity

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