Skip to Main Content

Isochronous Systems

Online ISBN:
9780191715853
Print ISBN:
9780199535286
Publisher:
Oxford University Press
Book

Isochronous Systems

Francesco Calogero
Francesco Calogero
Department of Physics, University of Rome "La Sapienza"
Find on
Published online:
1 May 2008
Published in print:
7 February 2008
Online ISBN:
9780191715853
Print ISBN:
9780199535286
Publisher:
Oxford University Press

Abstract

A classical dynamical system is called isochronous if it features in its phase space an open, fully dimensional sector where all its solutions are periodic in all their degrees of freedom with the same, fixed period. Recently, a simple transformation has been introduced, featuring a real parameter ω and reducing to the identity for ω=0. This transformation is applicable to a quite large class of dynamical systems and it yields ω-modified autonomous systems which are isochronous, with period T = 2π/ω. This justifies the notion that isochronous systems are not rare. In this monograph—which covers work done over the last decade by its author and several collaborators—this technology to manufacture isochronous systems is reviewed. Many examples of such systems are provided, including many-body problems characterized by Newtonian equations of motion in spaces of one or more dimensions, Hamiltonian systems, and also nonlinear evolution equations (PDEs: Partial Differential Equations). This monograph shall be of interest to researchers working on dynamical systems, including integrable and nonintegrable models, with a finite or infinite number of degrees of freedom. It shall also appeal to experimenters and practitioners interested in isochronous phenomena. It might be used as basic or complementary textbook for an undergraduate or graduate course.

Contents
Close
This Feature Is Available To Subscribers Only

Sign In or Create an Account

Close

This PDF is available to Subscribers Only

View Article Abstract & Purchase Options

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.

Close