Sufficient conditions for a partially hyperbolic attractor to be a homoclinic class

DOI10.1016/j.jde.2010.05.014zbMath1206.37017OpenAlexW2017388490MaRDI QIDQ710526

Carlos A. Morales

Publication date: 19 October 2010

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

Full work available at URL: https://doi.org/10.1016/j.jde.2010.05.014

zbMATH Keywords

homoclinic classhyperbolic periodic orbitLorenz-like singularitypartially hyperbolic attractor

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Partially hyperbolic systems and dominated splittings (37D30)

Related Items (2)

Robust attractors without dominated splitting on manifolds with boundary ⋮ The multidimensional Lorenz attractor is a homoclinic class

Cites Work

• Connecting invariant manifolds and the solution of the \(C^ 1\) stability and \(\Omega\)-stability conjectures for flows
• On the intersection of homoclinic classes on singular-hyperbolic sets
• The Sil'nikov problem, exponential expansion, strong \(\lambda\)-lemma, \(C^ 1\)-linearization, and homoclinic bifurcation
• Structural stability of Lorenz attractors
• Sufficient conditions for robustness of attractors
• A note on periodic orbits for singular-hyperbolic flows
• Dynamical properties of singular-hyperbolic attractors
• Singular hyperbolic systems
• Global aspects of homoclinic bifurcations of vector fields
• Invariant manifolds
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