Generic bi-Lyapunov stable homoclinic classes

DOI10.1088/0951-7715/23/7/006zbMath1198.37027arXiv0903.4090OpenAlexW2017918365MaRDI QIDQ3577802

Rafael Potrie

Publication date: 23 July 2010

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.4090

zbMATH Keywords

normal formscenter manifold theorybifurcation theoryhyperbolic orbits and setshomeomorphisms and diffeomorphisms of planes and surfacesnonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory)

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Generic properties, structural stability of dynamical systems (37C20) Partially hyperbolic systems and dominated splittings (37D30)

Related Items (12)

Dirac physical measures on saddle-type fixed points ⋮ Hyperbolicity versus weak periodic orbits inside homoclinic classes ⋮ On bi-Lyapunov stable homoclinic classes ⋮ Partially hyperbolic sets with a dynamically minimal lamination ⋮ Local perturbations of conservativeC¹diffeomorphisms ⋮ Unnamed Item ⋮ Orbital shadowing property on chain transitive sets for generic diffeomorphisms ⋮ Dirac physical measures for generic diffeomorphisms ⋮ Lyapunov stable homoclinic classes for smooth vector fields ⋮ Bi-Lyapunov stable homoclinic classes for \(C^1\) generic flows ⋮ A Franks’ lemma that preserves invariant manifolds ⋮ Uniform hyperbolicity along periodic orbits

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