2026-06-28T10:12:13Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/514622023-08-05T23:32:36Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Gómez-Ullate Otaiza, David
author
Hone, A.N.W.
author
Sommacal, M
2023-06-20T10:55:35Z
2023-06-20T10:55:35Z
2004-02-17
1367-2630
10.1088/1367-2630/6/1/024
https://hdl.handle.net/20.500.14352/51462
http://dx.doi.org/10.1088/1367-2630/6/1/024
http://iopscience.iop.org
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 greater than or equal to 4 Painleve 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.
eng
New many-body problems in the plane with periodic solutions
journal article
URL
https://docta.ucm.es/bitstreams/43cce80f-253d-4793-9341-1437b3b45c38/download
File
MD5
5f206b7764585b1e0d5819842d4aca5c
9174817
application/pdf
gomez-ullate28libre.pdf