portada Notes on Hamiltonian Dynamical Systems (London Mathematical Society Student Texts) (en Inglés)

Notes on Hamiltonian Dynamical Systems (London Mathematical Society Student Texts) (en Inglés)

Formato

Libro Físico

Autor

Antonio Giorgilli

Editorial

Cambridge University Press

Año

2022

Idioma

Inglés

N° páginas

460

Encuadernación

Tapa Dura

Dimensiones

22.9x15.2x2.5 cm

Peso

0.79 kg.

ISBN13

9781009151146

Categorías

Cálculo diferencial y ecuaciones
Física matemática

Notes on Hamiltonian Dynamical Systems (London Mathematical Society Student Texts) (en Inglés)

Antonio Giorgilli (Autor) · Cambridge University Press · Tapa Dura

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Reseña del libro "Notes on Hamiltonian Dynamical Systems (London Mathematical Society Student Texts) (en Inglés)"

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 Poincaré'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 Poincaré 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.