BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Small divisors and free vibrations in the n-vortex filament problem García Azpeitia, Carlos


In this talk we discuss families of homographic standing waves appearing from n vortex filaments rotating uniformly at a central configuration. The solution of the filaments are time periodic with periodic boundary conditions, i.e. this is a small divisor problem for a Hamiltonian partial differential equation which requires techniques related to KAM theory. In this case the Nash-Moser method gives rise to a family of solutions over a Cantor set of parameters. On the other hand, we show that when the relation between temporal and spatial periods is fixed at certain rational numbers, the contraction mapping theorem gives existence of an infinite number of families of standing waves that bifurcate from these configurations.

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