Robust transitivity and topological mixing for 𝐶¹-flows

DOI10.1090/S0002-9939-03-07187-9zbMath1040.37013arXivmath/0202207OpenAlexW3099859851MaRDI QIDQ4441780

Artur Avila, Flavio Abdenur, Jairo Bochi

Publication date: 7 January 2004

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0202207

zbMATH Keywords

topological mixingrobust transitive setshomoclinic classeshyperbolic basic setsgeneric properties of flows

Mathematics Subject Classification ID

Related Items (7)

On Peixoto’s conjecture for flows on non-orientable 2-manifolds ⋮ On \(C^1\)-generic chaotic systems in three-manifolds ⋮ Measure expansivity for \(C^1\)-conservative systems ⋮ A generic incompressible flow is topological mixing ⋮ Generic Hamiltonian dynamics ⋮ Robust transitivity of singular hyperbolic attractors ⋮ The dynamics of vector fields with singularities

Cites Work

• Connecting invariant manifolds and the solution of the \(C^ 1\) stability and \(\Omega\)-stability conjectures for flows
• Mixing Anosov flows
• On maximal transitive sets of generic diffeomorphisms
• A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources
• Mixing attractors for 3-flows
• Connexions hétéroclines et généricité d'une infinité de puits et de sources
• Approximation des ensembles ω-limites des difféomorphismes par des orbites périodiques
• An Improved Closing Lemma and a General Density Theorem

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