A triple boundary lemma for surface homeomorphisms
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- by Andres Koropecki, Patrice Le Calvez and Fabio Armando Tal PDF
- Proc. Amer. Math. Soc. 147 (2019), 681-686 Request permission
Abstract:
Given an orientation-preserving and area-preserving homeomorphism $f$ of the sphere, we prove that every point which is in the common boundary of three pairwise disjoint invariant open topological disks must be a fixed point. As an application, if $K$ is an invariant Wada-type continuum, then $f^n|_K$ is the identity for some $n>0$. Another application is an elementary proof of the fact that invariant disks for a nonwandering homeomorphism homotopic to the identity in an arbitrary surface are homotopically bounded if the fixed point set is inessential. The main results in this article are self-contained.References
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Additional Information
- Andres Koropecki
- Affiliation: Instituto de Matemática e Estatística, Universidade Federal Fluminense, Rua Mário Santos Braga S/N, 24020-140 Niteroi, RJ, Brazil
- MR Author ID: 856885
- Email: ak@id.uff.br
- Patrice Le Calvez
- Affiliation: Institut de Mathématiques de Jussieu-Paris Rive Gauche, IMJ-PRG, Sorbonne Université, Université Paris Diderot, CNRS, F-75005, Paris, France
- MR Author ID: 111345
- Email: patrice.le-calvez@imj-prg.fr
- Fabio Armando Tal
- Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090 São Paulo, SP, Brazil
- MR Author ID: 653938
- Email: fabiotal@ime.usp.br
- Received by editor(s): September 2, 2017
- Received by editor(s) in revised form: April 4, 2018
- Published electronically: November 8, 2018
- Additional Notes: The first author was partially supported by the German Research Council (Mercator fellowship, DFG-grant OE 538/9-1), as well as FAPERJ-Brasil and CNPq-Brasil.
The third author was partially supported by the Alexander Von Humboldt foundation and by FAPESP, CNPq and CAPES - Communicated by: Nimish Shah
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 681-686
- MSC (2010): Primary 37E30
- DOI: https://doi.org/10.1090/proc/14258
- MathSciNet review: 3894907