Asymptotically isochronous systems

Asymptotically isochronous systems

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 examp...

Isochronous dynamical systems.

This is a terse review of recent results on isochronous dynamical systems, namely systems of (first-order, generally nonlinear) ordinary differential equations (ODEs) featuring an open set of initial data (which might coincide with the entire set of all initial data), from which emerge solutions all of which are completely periodic (i.e. periodic in all their components) with a fixed period (in...

Isochronous Systems and Perturbation Theory

This article displays examples of planar isochronous systems and discuss the new techniques found by F. Calogero with these examples. A sufficient condition is found to keep track of some periodic orbits for perturbations of isochronous systems.

Recursive Generation of Isochronous Hamiltonian Systems

We propose a simple procedure to identify the collective coordinate Q which is used to generate the isochronous Hamiltonian. The new isochronous Hamiltonian generates more and more isochronous oscillators, recursively. In recent years considerable interest has been shown to identify and classify isochronous systems. In this direction Calogero and his coworkers have introduced a number of system...

Isochronous sets of invariant control systems