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arXiv · 0710.1487

Asymptotically isochronous systems

Francesco Calogero·David Gomez-Ullate
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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 asymptotically to functions periodic with the same 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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Francesco Calogero, David Gomez-Ullate. 2007-10-08. Asymptotically isochronous systems. https://doi.org/10.2991/jnmp.2008.15.4.5

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