Isochronous Systems

Paperback | October 20, 2012

byFrancesco Calogero

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A dynamical system is called isochronous if it features in its phase space an open, fully-dimensional region where all its solutions are periodic in all its degrees of freedom with the same, fixed period. Recently a simple transformation has been introduced, applicable to quite a large classof dynamical systems, that yields autonomous systems which are isochronous. This justifies the notion that isochronous systems are not rare.In this book the procedure to manufacture isochronous systems is reviewed, and many examples of such systems are provided. Examples include many-body problems characterized by Newtonian equations of motion in spaces of one or more dimensions, Hamiltonian systems, and also nonlinear evolutionequations (PDEs).The book shall be of interest to students and researchers working on dynamical systems, including integrable and nonintegrable models, with a finite or infinite number of degrees of freedom. It might be used as a basic textbook, or as backup material for an undergraduate or graduate course.

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From the Publisher

A dynamical system is called isochronous if it features in its phase space an open, fully-dimensional region where all its solutions are periodic in all its degrees of freedom with the same, fixed period. Recently a simple transformation has been introduced, applicable to quite a large classof dynamical systems, that yields autonomous ...

Francesco Calogero is Professor of Theoretical Physics in the Department of Physics at the University of Rome "La Sapienza".

other books by Francesco Calogero

Format:PaperbackDimensions:264 pages, 9.21 × 6.14 × 0.68 inPublished:October 20, 2012Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199657521

ISBN - 13:9780199657520

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Table of Contents

1. Introduction2. Isochronous systems are not rare3. A single ODE of arbitrary order4. Systems of ODEs: many-body problems, nonlinear harmonic oscillators5. Isochronous Hamiltonian systems are not rare6. Asymptotically isochronous systems7. Isochronous PDEs8. OutlookAppendix A: Some useful identitiesAppendix B: Two proofsAppendix C: Diophantine findings and conjectures

Editorial Reviews

"The book is full of character and written in a colloquial manner. Overall, I did enjoy reading this book and I warmly recommend it to all researchers interested in dynamical systems, in particular integrable and super-integrable systems." --Cristina Stoica, Mathematical Reviews