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SUMMARY:Matthias Meiwes (RWTH Aachen University)
DTSTART:20220601T111000Z
DTEND:20220601T123000Z
DTSTAMP:20260423T024532Z
UID:GDS/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDS/61/">Ent
 ropy\, braids\, and Hofer's metric</a>\nby Matthias Meiwes (RWTH Aachen Un
 iversity) as part of Geometry and Dynamics seminar\n\n\nAbstract\nTopologi
 cal entropy captures the orbit complexity of a dynamical system with \nthe
  help of a single non-negative number. Detecting robustness of this number
  \nunder perturbation is a way to understand stability features of a chaot
 ic system.\nIn my talk\, I will address the problem of robustness of entro
 py for Hamiltonian \ndiffeomorphisms in terms of Hofer's metric. Our main 
 focus lies on dimension 2\, \nwhere there is a strong connection between t
 opological entropy and the existence \nof specific braid types of periodic
  orbits. I explain that the construction of \neggbeater maps of Polterovic
 h-Shelukhin and their generalizations by Chor provide \nrobustness even un
 der large perturbation: the entropy will not drop much when \nperturbing t
 he specific diffeomorphism in some ball of large Hofer-radius. \nI further
 more discuss a result that any braid of non-degenerate one-periodic \norbi
 ts with pairwise homotopic strands persists under generic Hofer-small \npe
 rturbations\, which yields a local entropy robustness result for surfaces.
 \nThis talk is based on joint works with Arnon Chor\, and Marcelo Alves.\n
LOCATION:https://researchseminars.org/talk/GDS/61/
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