Volume 10, Issue 2, May 2003, Pages 157 - 214
Periodic Solutions of a Many-Rotator Problem in the Plane. II. Analysis of Various Motions
F CALOGERO, J-P FRANC¸OISE, M SOMMACAL
Received 13 May 2002, Accepted 2 August 2002, Available Online 1 May 2003.
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- Various solutions are displayed and analyzed (both analytically and numerically) of a recently-introduced many-body problem in the plane which includes both integrable and nonintegrable cases (depending on the values of the coupling constants); in paticular the origin of certain periodic behaviors is explained. The light thereby shone on the connection among integrability and analyticity in (complex) time, as well as on the emergence of a chaotic behavior (in the guise of a sensitive dependance on the initial data) not associated with any local exponential divergence of trajectories in phase space, might illuminate interesting phenomena of more general validity than for the particular model considered herein.
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Cite this article
TY - JOUR AU - F CALOGERO AU - J-P FRANC¸OISE AU - M SOMMACAL PY - 2003 DA - 2003/05 TI - Periodic Solutions of a Many-Rotator Problem in the Plane. II. Analysis of Various Motions JO - Journal of Nonlinear Mathematical Physics SP - 157 EP - 214 VL - 10 IS - 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2003.10.2.4 DO - https://doi.org/10.2991/jnmp.2003.10.2.4 ID - CALOGERO2003 ER -