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Home » Hamiltonian Postdoc Workshop: Equilibrium quasi-periodic configurations in quasi-periodic media

Seminar

Hamiltonian Postdoc Workshop: Equilibrium quasi-periodic configurations in quasi-periodic media November 14, 2018 (01:15 PM PST - 02:05 PM PST)
Parent Program:
Location: MSRI: Simons Auditorium
Speaker(s) Lei Zhang (University of Toronto, Mississauga)
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Abstract/Media

We consider a quasi-periodic version of the well-known Frenkel-Kontorova

model and looking for quasi-periodic equilibria with a frequency that resonates with the

frequencies of the medium. We show that there are always perturbative expansions and

prove a KAM theorem in a-posteriori form. We show that if there is an approximate

solution of the equilibrium equation satisfying non-degeneracy conditions, we can adjust

one parameter and obtain a true solution which is close to the approximate solution. The

proof is based on an iterative method of the KAM type.

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