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Robust transitivity for endomorphisms admitting critical points


Authors: J. Iglesias, C. Lizana and A. Portela
Journal: Proc. Amer. Math. Soc. 144 (2016), 1235-1250
MSC (2010): Primary 37D20, 37D30, 08A35, 35B38
DOI: https://doi.org/10.1090/proc/12799
Published electronically: October 14, 2015
MathSciNet review: 3447675
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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.


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J. Iglesias
Affiliation: Facultad de Ingenieria, IMERL, Universidad de La República, Julio Herrera y Reissig 565, C.P. 11300, Montevideo, Uruguay
Email: jorgei@fing.edu.uy

C. Lizana
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de los Andes, La Hechicera-Mérida 5101, Venezuela
Email: clizana@ula.ve

A. Portela
Affiliation: Facultad de Ingenieria, IMERL, Universidad de La República, Julio Herrera y Reissig 565, C.P. 11300.,Montevideo, Uruguay
Email: aldo@fing.edu.uy

DOI: https://doi.org/10.1090/proc/12799
Keywords: Robustly transitive endomorphisms, critical set
Received by editor(s): August 5, 2014
Received by editor(s) in revised form: March 17, 2015
Published electronically: October 14, 2015
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society