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UID:bef8047bdb857722d4c400151212d9ce
CATEGORIES:Colloquia
CREATED:20230206T092322
SUMMARY:Computational methods for global dynamics
LOCATION:Hill Center 705
DESCRIPTION:Abstract: We survey computational methods for approximating the global long
 -term behavior of dynamical systems.  We will see how to approximate sets o
 f states which remain invariant under the dynamics and how to use these app
 roximations in order to prove the existence of symbolic dynamics. We will t
 hen construct a linear operator which, similar to the Koopman operator, des
 cribes the evolution of probability densities on the state space.  The eige
 nfunctions of this operator will reveal certain macroscopic features of the
  dynamics.  For finite-time and time-varying dynamical systems this concept
  can be adapted and leads to a method for the computation of advective cohe
 rent sets (e.g. eddies in an unsteady fluid flow). We will see how these se
 ts can actually be computed from sparse and incomplete trajectory data alon
 e. Throughout the talk, the mathematical concepts will be illustrated by co
 mputational examples.\n
X-ALT-DESC;FMTTYPE=text/html:<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:20260827T094947
DTSTART;TZID=America/New_York:20230210T160000
DTEND;TZID=America/New_York:20230210T170000
SEQUENCE:0
TRANSP:OPAQUE
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