Notes on Hamiltonian Dynamical Systems

ISBN-13: 9781009151139 / Angielski / Miękka / 2022

Antonio Giorgilli

Opis

Introduces Hamiltonian dynamics from the very beginning, culminating in the most important recent results: Kolmogorov's and Nekhoroshev's.

Recenzje

'The author provides a treatment that is accessible to newcomers, complete, and attentive to the complexities of the subject's historical development. One of the appeals of the book is the way it mixes the technical details of formal statements and proofs with numerical experiments and historical digression … The book covers a great deal of material, but it does so gracefully and thoroughly.' Bill Satzer, MAA Reviews

Spis treści

1. Hamiltonian formalism; 2. Canonical transformations; 3. Integrable systems; 4. First integrals; 5. Nonlinear oscillations; 6. The method of Lie series and of Lie transform; 7. The normal form of Poincaré and Birkhoff; 8. Persistence of invariant tori; 9. Long time stability; 10. Stability and chaos; A. The geometry of resonances; B. A quick introduction to symplectic geometry; References; Index.