Séminaires : Séminaire Géométrie et Topologie

Ce séminaire s’adresse aux géomètres, topologues et dynamiciens au sens large. Il est rattaché aux équipes Analyse Algébrique et Analyse Complexe et Géométrie. Les exposés seront accessibles à une audience large, doctorants inclus. Il se tiendra à Jussieu, le jeudi à 11h, en salle 15-25 502. Le séminaire a l'agenda google suivante: https://calendar.google.com/calendar/b/0?cid=dDgzNTJoczNmdDhlMm5nb2IzMXJwaWpsdHNAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ

We study homeomorphisms of the open annulus from a topological perspective, introducing simple computable criteria related to mild twist conditions (pair of periodic points with different rotation numbers), which implies the existence of rotational horseshoes and so positive topological entropy. As consequences, we obtain applications in surface dynamics including a final answer to a classical conjecture, showing that the existence of an invariant circloid with nontrivial rotation set implies chaos. Moreover, quantitative versions of the results can be used for numerical proofs of the existence of chaos, both in the conservative and dissipative settings.

J. with A. Passeggi