How to Extend any Dynamical System so That it Becomes Isochronous, Asymptotically Isochronous or Multi-Periodic

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 Potentials

Control System of the Small Isochronous Ring*

The purpose of this paper is to describe the control system of the Small Isochronous Ring (SIR) developed and built at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University (MSU). SIR is a small-scale experiment that simulates the dynamics of intense beams in large accelerators. A 20 to 30 keV hydrogen or deuterium ion bunch is injected in the ring, extracted aft...

Quasi-isochronous storage ring

In tins article we study the possibility of designing storage rings with a reduced by two or more orders of magnitude with respect to existing rings, thus making the bunch length shorter by a factor of 10 or more . We will, with an appropriate design, show that this bunch length reduction can be achieved while simultaneously increasing the beam peak current. With this approach one can increase ...