Robust transitivity for endomorphisms admitting critical points

DOI10.1090/proc/12799zbMath1354.37036arXiv1408.1661OpenAlexW2963061171MaRDI QIDQ2790200

Cristina Lizana, Jorge Iglesias, Aldo Portela

Publication date: 3 March 2016

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

Full work available at URL: https://arxiv.org/abs/1408.1661

zbMATH Keywords

critical setrobustly transitive endomorphisms

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Partially hyperbolic systems and dominated splittings (37D30) Automorphisms and endomorphisms of algebraic structures (08A35)

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Topological obstructions for robustly transitive endomorphisms on surfaces, An example of a map which is $C^2$-robustly transitive but not $C^1$-robustly transitive, A persistently singular map of $\mathbb{T}^n$ that is $C^2$ robustly transitive but is not $C^1$ robustly transitive, SRB measures for partially hyperbolic attractors of local diffeomorphisms, Robust transitivity and domination for endomorphisms displaying critical points, A persistently singular map of $\mathbb{T}^n$ that is $C^1$ robustly transitive

Cites Work

• Contribution to the ergodic theory of robustly transitive maps
• On singularities of mappings of Euclidean spaces. I. Mappings of the plane into the plane
• Contributions to the stability conjecture
• A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources
• An ergodic closing lemma
• On the inverse limit stability of endomorphisms
• Robustly non-hyperbolic transitive endomorphisms on 𝕋²
• Robust transitivity for endomorphisms