On the inverse limit stability of endomorphisms

DOI10.1016/j.anihpc.2012.10.001zbMath1373.37096arXiv1006.4302OpenAlexW2963776302MaRDI QIDQ2450584

Pierre Berger, Alvaro Rovella

Publication date: 14 May 2014

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.4302

zbMATH Keywords

hyperbolicitystrong transversality condition\(C^1\)-inverse stabilityAxiom \(A\)

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Stability theory for smooth dynamical systems (37C75) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (13)

Topological obstructions for robustly transitive endomorphisms on surfaces ⋮ Generic family with robustly infinitely many sinks ⋮ On the unstable directions and Lyapunov exponents of Anosov endomorphisms ⋮ An example of a map which is $C^2$-robustly transitive but not $C^1$-robustly transitive ⋮ Lectures on structural stability in dynamics ⋮ Germ-typicality of the coexistence of infinitely many sinks ⋮ A persistently singular map of $\mathbb{T}^n$ that is $C^2$ robustly transitive but is not $C^1$ robustly transitive ⋮ Structural stability of the inverse limit of endomorphisms ⋮ Anosov endomorphisms on the two-torus: regularity of foliations and rigidity ⋮ Rigidity for some cases of Anosov endomorphisms of torus ⋮ Robust transitivity and domination for endomorphisms displaying critical points ⋮ Robust transitivity for endomorphisms admitting critical points ⋮ A persistently singular map of $\mathbb{T}^n$ that is $C^1$ robustly transitive

Cites Work

• Persistence of laminations
• Persistence of stratifications of normally expanded laminations
• A proof of the \(C^ 1\) stability conjecture
• Structural stability of \(C^1\) diffeomorphisms
• Laminations in holomorphic dynamics
• Density of hyperbolicity in dimension one
• C¹-maps having hyperbolic periodic points
• C¹stable maps: examples without saddles
• Stability of Anosov Maps
• On Ω-stability and structural stability of endomorphisms satisfying Axiom A
• Anosov endomorphisms
• Periodic Points and Measures for Axiom a Diffeomorphisms
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