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On a class of many-body problems in the plane (including integrable and nonintegrable cases) which possess a lot of periodic solutions

Presented by: 
F Calogero [Rome]
Date: 
Wednesday 10th October 2001 - 15:00 to 16:00
Venue: 
INI Seminar Room 1
Abstract: 
A class of many-body problems in the plane, characterised by translation- and rotation-invariant Newtonian equations of motion (derivable from a Hamiltonian), and including both integrable and (presumably) nonintegrable cases, is shown to possess lots of completely periodic solutions (emerging from open sets of initial data having nonvanishing measure in phase space). The mechanism whereby this happens is elucidated; the light thereby shone on the connection among integrability and analyticity in (complex) time, as well as on the emergence of a chaotic behavior not associated with any local exponential divergence of trajectories in phase space, illuminates interesting phenomena of more general validity than for the particular model considered herein.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons