Non UBC
DSpace
Carlos GarcĂa Azpeitia
2019-12-10T09:20:33Z
2019-06-12T09:51
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.
https://circle.library.ubc.ca/rest/handle/2429/72636?expand=metadata
40.0 minutes
video/mp4
Author affiliation: UNAM
Oaxaca (Mexico : State)
10.14288/1.0386831
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Faculty
BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))
Mathematics
Dynamical Systems And Ergodic Theory, Partial Differential Equations
Small divisors and free vibrations in the n-vortex filament problem
Moving Image
http://hdl.handle.net/2429/72636