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OverviewA 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. Full Product DetailsAuthor: "Francesco Calogero (Department of Physics, University of Rome ""La Sapienza"")"Publisher: Oxford University Press Imprint: Oxford University Press Dimensions: Width: 16.80cm , Height: 1.40cm , Length: 23.40cm Weight: 0.406kg ISBN: 9780199657520ISBN 10: 0199657521 Pages: 264 Publication Date: 20 September 2012 Audience: College/higher education , Postgraduate, Research & Scholarly , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of Contents1: 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 conjecturesReviewsAn 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 Author Information"Francesco Calogero, Department of Physics, University of Rome ""La Sapienza""" Tab Content 6Author Website:Countries AvailableAll regions |
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