Publication: Asymptotically isochronous systems
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2008-12
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Atlantis Press
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Abstract
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotic ally to functions periodic with the sa m e fixed period. We focus on two such mechanisms, emphasizing their generality and illustrating each of them via a representative example. The first example belongs to a recently discovered class of integrable indeed solvable many-body problems. The second example consists of a broad class of (generally nonintegrable) models obtained by deforming appropriately the well-known (integrable and isochronous) many-body problem with inverse-cube two-body forces and a one-body linear ("harmonic oscillator") force.
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© Atlantis Press.
One of us (FC) would like to thank Francois Leyvraz for several illuminating discussions. The research reported in this paper has profited from visits by each of the two authors in the Department of the other performed in the framework of the exchange program among our two Universities. The research of DGU is supported in part by the Ramón y Cajal program of the Ministerio de Ciencia y Tecnología and by the DGI under grants FIS2005-00752 and MTM2006-00478.
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