Robust transitivity for endomorphisms admitting critical points-Reference-Cited by-同舟云学术

Robust transitivity for endomorphisms admitting critical points

Published:2015-10-14 Issue:3 Volume:144 Page:1235-1250
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Iglesias J.,Lizana C.,Portela A.

Abstract

We address the problem of giving necessary and sufficient conditions in order to have robustly transitive endomorphisms admitting persistent critical sets. We exhibit different types of open examples of robustly transitive maps in any isotopic class of endomorphisms acting on the two dimensional torus admitting persistent critical points. We also provide some necessary conditions for robust transitivity in this setting.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2016-144-03/S0002-9939-2015-12799-2/S0002-9939-2015-12799-2.pdf

Reference9 articles.

1. On the inverse limit stability of endomorphisms;Berger, Pierre;Ann. Inst. H. Poincar\'{e} Anal. Non Lin\'{e}aire,2013

2. A 𝐶¹-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks or sources;Bonatti, C.;Ann. of Math. (2),2003

3. Robustly non-hyperbolic transitive endomorphisms on 𝕋²;He, Baolin;Proc. Amer. Math. Soc.,2013

4. Robust transitivity for endomorphisms;Lizana, Cristina;Ergodic Theory Dynam. Systems,2013

5. Contribution to the ergodic theory of robustly transitive maps;Lizana, Cristina;Discrete Contin. Dyn. Syst.,2015

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. New classes of C ¹ -robustly transitive maps with persistent critical points;Dynamical Systems;2024-01-25

2. Robust transitivity and domination for endomorphisms displaying critical points;Ergodic Theory and Dynamical Systems;2023-04-14

3. A persistently singular map of $\mathbb{T}^n$ that is $C^1$ robustly transitive;Bulletin de la Société mathématique de France;2021-12-10

4. Topological obstructions for robustly transitive endomorphisms on surfaces;Advances in Mathematics;2021-10

5. A PERSISTENTLY SINGULAR MAP OF T-n THAT IS C-2 ROBUSTLY TRANSITIVE BUT IS NOT C-1 ROBUSTLY TRANSITIVE;J KOREAN MATH SOC;2021