New many-body problems in the plane with periodic solutions

Gomez-Ullate, David, Hone, Andy and Sommacal, Matteo (2004) New many-body problems in the plane with periodic solutions. New Journal of Physics, 6. p. 24. ISSN 1367-2630

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In this paper we discuss a family of toy models for many-body interactions including velocity-dependent forces. By generalizing a construction due to Calogero, we obtain a class of N-body problems in the plane which have periodic orbits for a large class of initial conditions. The two- and three-body cases (N=2, 3) are exactly solvable, with all solutions being periodic, and we present their explicit solutions. For N≥4 Painlevé analysis indicates that the system should not be integrable, and some periodic and non-periodic trajectories are calculated numerically. The construction can be generalized to a broad class of systems, and the mechanism which describes the transition to orbits with higher periods, and eventually to aperiodic or even chaotic orbits, could be present in more realistic models with a mixed phase space. This scenario is different from the onset of chaos by a sequence of Hopf bifurcations.

Item Type: Article
Uncontrolled Keywords: mathematical physics, statistical physics and nonlinear systems
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Related URLs:
Depositing User: Matteo Sommacal
Date Deposited: 09 May 2012 14:12
Last Modified: 13 Oct 2019 00:22

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