Isochronous Systems
1st Edition
Published on 20. September 2012
Book
Paperback/Softback
264 pages
978-0-19-965752-0 (ISBN)
Description
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 class of 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 evolution equations (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.
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 evolution equations (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.
Reviews / Votes
An interesting reading offering the possibility to explore a new and beautiful direction. * Adrian Constantin, University of Lund * 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 *More details
Language
English
Place of publication
Oxford
United Kingdom
Target group
College/higher education
Graduate students in physics and mathematics. Mathematical physicists and applied mathematicians, and practitioners working with dynamical systems and isochronous phenomena.
Illustrations
2 b/w line drawings
Dimensions
Height: 234 mm
Width: 168 mm
Thickness: 14 mm
Weight
406 gr
ISBN-13
978-0-19-965752-0 (9780199657520)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Francesco Calogero
Isochronous Systems
Book
02/2008
Oxford University Press
€51.00
Shipment within 15-20 days
Person
Francesco Calogero, Department of Physics, University of Rome "La Sapienza"
Content
1. Introduction ; 2. Isochronous systems are not rare ; 3. A single ODE of arbitrary order ; 4. Systems of ODEs: many-body problems, nonlinear harmonic oscillators ; 5. Isochronous Hamiltonian systems are not rare ; 6. Asymptotically isochronous systems ; 7. Isochronous PDEs ; 8. Outlook ; Appendix A: Some useful identities ; Appendix B: Two proofs ; Appendix C: Diophantine findings and conjectures