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UID:bef8047bdb857722d4c400151212d9ce
CATEGORIES:Colloquia
CREATED:20230206T092322
SUMMARY:Computational methods for global dynamics
LOCATION:Hill Center 705
DESCRIPTION:<p style="background: white;">Abstract: We survey computational methods for
  approximating the global long-term behavior of dynamical systems. &nbsp;We
  will see how to approximate sets of states which remain invariant under th
 e dynamics and how to use these approximations in order to prove the existe
 nce of symbolic dynamics. We will then construct a linear operator which, s
 imilar to the Koopman operator, describes the evolution of probability dens
 ities on the state space. &nbsp;The eigenfunctions of this operator will re
 veal certain macroscopic features of the dynamics. &nbsp;For finite-time an
 d time-varying dynamical systems this concept can be adapted and leads to a
  method for the computation of advective coherent sets (e.g. eddies in an u
 nsteady fluid flow). We will see how these sets can actually be computed fr
 om sparse and incomplete trajectory data alone. Throughout the talk, the ma
 thematical concepts will be illustrated by&nbsp;computational examples.</p>
CONTACT:Oliver Junge (TU Munich) 
DTSTAMP:20260828T015309
DTSTART;TZID=America/New_York:20230210T160000
DTEND;TZID=America/New_York:20230210T170000
SEQUENCE:0
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