Asymptotically isochronous systems

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.

18 pages, 3 figures

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Cited by in corpus (6)

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• Solution of the system of two coupled first-order ODEs with second-degree polynomial right-hand sides
• Polynomials with Multiple Zeros and Solvable Dynamical Systems including Models in the Plane with Polynomial Interactions
• Time-dependent polynomials with one multiple root and new solvable dynamical systems
• Poisson Structures for Aristotelian Model of Three Body Motion