Séminaire Analyse Numérique et EDP
Internal waves in 2D aquaria and homeomorphisms of the circle
16
déc. 2021
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Intervenant : Maciej Zworski
Institution : UC Berkeley
Heure : 15h30 - 16h30
Lieu : 3L8
The connection between the formation of internal waves in
fluids, spectral theory, and homeomorphisms of the circle was investigated by
oceanographers in the 90s and resulted in novel experimental
observations (Maas et al, 1997). The specific homeomorphism is given
by a ``chess billiard" and has been considered by many authors (John
1941, Arnold 1957... ). The relation between the nonlinear dynamics of
this homeomorphism and linearized internal waves provides a striking
example of classical/quantum correspondence (in a classical and
surprising setting of fluids!).

I will illustrate the results with numerical examples and explain how
classical concepts such as rotation numbers of diffeomorphisms
(introduced by Poincare)
are related to solutions of the Poincare evolution problem.

The talk is based on joint work with S Dyatlov and J Wang.
Nicolas Burq
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