OXFORD UNIVERSITY PRESS

Isochronous Systems

ISBN : 9780199657520

参考価格(税込): 
¥9,493
著者: 
Francesco Calogero
ページ
264 ページ
フォーマット
Paperback
サイズ
168 x 234 mm
刊行日
2012年09月
メール送信
印刷

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.

目次: 

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

著者について: 

Francesco Calogero, Department of Physics, University of Rome La Sapienza

このページに掲載の「参考価格」は日本国内における希望小売価格です。当ウェブサイトでのご購入に対して特別価格が適用される場合、販売価格は「割引価格」として表示されます。なお、価格は予告なく変更されることがございますので、あらかじめご了承ください。