An example of a map which is $C^2$-robustly transitive but not $C^1$-robustly transitive

DOI10.4064/CM7131-5-2017zbMath1393.37055arXiv1606.07048OpenAlexW2963982234MaRDI QIDQ4565094

Aldo Portela, Jorge Iglesias

Publication date: 7 June 2018

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.07048

zbMATH Keywords

critical settransitive endomorphism

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Partially hyperbolic systems and dominated splittings (37D30) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (3)

A persistently singular map of $\mathbb{T}^n$ that is $C^2$ robustly transitive but is not $C^1$ robustly transitive ⋮ 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

• Unnamed Item
• 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
• Robust transitivity for endomorphisms admitting critical points
• Robustly non-hyperbolic transitive endomorphisms on 𝕋²
• Robust transitivity for endomorphisms

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