Buch, Englisch, 264 Seiten, Format (B × H): 168 mm x 234 mm, Gewicht: 406 g
Buch, Englisch, 264 Seiten, Format (B × H): 168 mm x 234 mm, Gewicht: 406 g
ISBN: 978-0-19-965752-0
Verlag: Oxford University Press
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.
Zielgruppe
Graduate students in physics and mathematics. Mathematical physicists and applied mathematicians, and practitioners working with dynamical systems and isochronous phenomena.
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
Weitere Infos & Material
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
