Partial hyperbolicity and robust transitivity

DOI10.1007/BF02392945zbMath0987.37020OpenAlexW2046851121MaRDI QIDQ1588919

Raúl Ures, Enrique R. Pujals, Lorenzo J. Dıaz

Publication date: 6 December 2000

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02392945

zbMATH Keywords

compact manifoldrobust transitivity

Mathematics Subject Classification ID

Generic properties, structural stability of dynamical systems (37C20) Partially hyperbolic systems and dominated splittings (37D30)

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Cites Work

• Unnamed Item
• Connecting invariant manifolds and the solution of the \(C^ 1\) stability and \(\Omega\)-stability conjectures for flows
• A proof of the \(C^ 1\) stability conjecture
• Contributions to the stability conjecture
• High dimension diffeomorphisms displaying infinitely many periodic attractors
• Stably ergodic diffeomorphisms
• Sinai–Ruelle–Bowen measures for N-dimensional derived from Anosov diffeomorphisms
• Persistent Manifolds are Normally Hyperbolic
• On C1 robust singular transitive sets for three-dimensional flows
• Non-critical saddle-node cycles and robust non-hyperbolic dynamics
• Robust nonhyperbolic dynamics and heterodimensional cycles
• Persistence of homoclinic tangencies in higher dimensions
• Persistence of cycles and nonhyperbolic dynamics at heteroclinic bifurcations
• The Closing Lemma
• Differentiable dynamical systems
• On Codimension One Anosov Diffeomorphisms
• Necessary Conditions for Stability of Diffeomorphisms
• Composite differentiable functions
• Invariant manifolds

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