New cw-expansive homeomorphisms of surfaces

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

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.

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