| Titre : |
Notes on Hamiltonian Dynamical Systems |
| Type de document : |
texte imprimé |
| Auteurs : |
Antonio Giorgilli, Auteur |
| Editeur : |
Cambridge ; New York ; Melbourne [UK ; USA] : Cambridge University Press (CUP) |
| Année de publication : |
2022, cop. 2022 |
| Collection : |
London Mathematical Society student texts num. 102 |
| Importance : |
1 vol. (xix, 451 p.) |
| Présentation : |
ill. en coul. |
| Format : |
23 cm |
| ISBN/ISSN/EAN : |
978-1-00-915113-9 |
| Note générale : |
ISBN-10 : 1009151134 - ISBN-13 : 978-1009151139 .- PPN 263815501 |
| Langues : |
Anglais (eng) |
| Tags : |
Systèmes hamiltoniens Systèmes dynamiques Hamiltonian systems Differentiable dynamical systems |
| Index. décimale : |
515.39 Systèmes dynamiques (mathématiques), systèmes hamiltoniens , la théorie du chaos |
| Résumé : |
Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov-Arnold-Moser theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows students to learn about perturbation methods leading to advanced results. Key topics covered include Liouville's theorem, the proof of Poincare?'s non-integrability theorem and the nonlinear dynamics in the neighbourhood of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the theory of exponential stability of Nekhoroshev are proved via constructive algorithms based on the Lie series method. A final chapter is devoted to the discovery of chaos by Poincare? and its relations with integrability, also including recent results on superexponential stability. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students.(4ème de couverture) |
| Note de contenu : |
Bibliogr. p. [429]-443). Index sujet p.[445]-451
Sommaire : 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 Poincare 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 |
Notes on Hamiltonian Dynamical Systems [texte imprimé] / Antonio Giorgilli, Auteur . - Cambridge ; New York ; Melbourne (UK ; USA) : Cambridge University Press (CUP), 2022, cop. 2022 . - 1 vol. (xix, 451 p.) : ill. en coul. ; 23 cm. - ( London Mathematical Society student texts; 102) . ISBN : 978-1-00-915113-9 ISBN-10 : 1009151134 - ISBN-13 : 978-1009151139 .- PPN 263815501 Langues : Anglais ( eng)
| Tags : |
Systèmes hamiltoniens Systèmes dynamiques Hamiltonian systems Differentiable dynamical systems |
| Index. décimale : |
515.39 Systèmes dynamiques (mathématiques), systèmes hamiltoniens , la théorie du chaos |
| Résumé : |
Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov-Arnold-Moser theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows students to learn about perturbation methods leading to advanced results. Key topics covered include Liouville's theorem, the proof of Poincare?'s non-integrability theorem and the nonlinear dynamics in the neighbourhood of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the theory of exponential stability of Nekhoroshev are proved via constructive algorithms based on the Lie series method. A final chapter is devoted to the discovery of chaos by Poincare? and its relations with integrability, also including recent results on superexponential stability. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students.(4ème de couverture) |
| Note de contenu : |
Bibliogr. p. [429]-443). Index sujet p.[445]-451
Sommaire : 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 Poincare 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 |
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