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New cw-expansive homeomorphisms of surfaces
M. Achigar1 ; A. Artigue1 ; J. Vieitez1
1 Departamento de Matemática y Estadística del Litoral Universidad de la República Gral. Rivera 1350, Salto (Uruguay)
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 2, pp. 221-246.

Dans ce travail on caractérise les extensions monotones d’homéomorphismes cw-expansifs d’espaces métriques compacts. Pour faire cela, on introduit la notion de “demi cw-expansivité” et on étudie son espace quotient naturel, notament dans le cas de surfaces compactes. On utilise ses résultats pour construire des exemples nouveaux d’homomémorphismes cw-expansifs avec un nombre infini de points fixes et dont l’ensemble errant est vide, dans le cadre des surfaces. Ces exemples sont des quotients de perturbations topologiques de pseudo-Anosov diffeomorphismes. Nous montrons également qu’il existe un homéomorphisme cw-expansif du 2-sphère avec la propriété shadowing.

In this article we characterize monotone extensions of cw-expansive homeomorphisms of compact metric spaces. For this purpose we introduce the notion “half cw-expansivity” and we study its natural quotient space, specially in the case of compact surfaces. These results are applied to construct new examples of cw-expansive homeomorphisms of compact surfaces with infinitely many fixed points and empty wandering set. These examples are quotients of topological perturbations of pseudo-Anosov diffeomorphisms. We also show that there is a cw-expansive homeomorphism with the shadowing property of the 2-sphere.

Reçu le :
Accepté le :
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DOI : 10.5802/afst.1630

M. Achigar 1 ; A. Artigue 1 ; J. Vieitez 1

1 Departamento de Matemática y Estadística del Litoral Universidad de la República Gral. Rivera 1350, Salto (Uruguay)
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {New cw-expansive homeomorphisms of surfaces},
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     pages = {221--246},
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M. Achigar; A. Artigue; J. Vieitez. New cw-expansive homeomorphisms of surfaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 2, pp. 221-246. doi : 10.5802/afst.1630. https://afst.centre-mersenne.org/articles/10.5802/afst.1630/

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