Jeff Xia
(Department of Mathematics, Northwestern University)
Instability and Arnold Diffusion
in Hamiltonian Dynamics
Abstract
Arnold conjectured that a typical near-integrable Hamiltonian system of
high dimension is topologically unstable. These instabilities are results
of the phenomenon called Arnold diffusion. In this talk, we will explore
recent progresses in the area and particularly with regard to variational
approaches and Mather measures. We will show that indeed Arnold's conjecture
is true in most interesting cases.
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