This book will 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 can be used as a textbook or as background reading for an undergraduate or graduate course.

Francesco Calogero
Professor of Theoretical Physics, University of Rome "La Sapienza"

• 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