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SUMMARY:Symplectic Mather theory
DTSTART;VALUE=DATE-TIME:20180504T083000Z
DTEND;VALUE=DATE-TIME:20180504T093000Z
DTSTAMP;VALUE=DATE-TIME:20191014T214253Z
UID:indico-event-3452@indico.math.cnrs.fr
DESCRIPTION:I will discuss two different approaches to systematically stud
ying invariant sets of Hamiltonian systems. The first approach builds heav
ily on results due to Viterbo and Vichery. I will discuss how an analogue
of Mather's alpha-function arises from homogenized Floer homological Lagra
ngian spectral invariants and how it gives rise to the existence of an ana
logue of Mather measures (from Aubry-Mather theory) to general symplectic
manifolds. Unlike what happens in the Tonelli case\, I will show that the
support of these measures can be extremely "wild" in the non-convex case.
I will explain how this phenomenon is closely related to diffusion phenome
na such as Arnold' diffusion. The second approach builds on work due to Bu
hovsky-Entov-Polterovich and provides a C^0-analogue of Mather measures fo
r Hamiltonians on "flexible" symplectic manifolds. I will discuss applicat
ions to Hamiltonian systems on twisted cotangent bundles and R^2n.\n\nhttp
s://indico.math.cnrs.fr/event/3452/
LOCATION:ICJ Salle 112
URL:https://indico.math.cnrs.fr/event/3452/
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