Asymptotically isochronous systems

Details Asymptotically isochronous systems Asymptotically isochronous systems

2007-10-08

arxiv.org/abs/0710.1487v1

J. Nonlin. Math. Phys. 15 (2008) 410-426

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages, 3 figures

Scientific paper

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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