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Advanced Hamiltonian Dynamics and Arnold Diffusion

Name: Advanced Hamiltonian Dynamics and Arnold Diffusion
Brand: Springer, Berlin
SKU: 9789819559640
Price: 164.23 EUR
Availability: InStock

Autor: Chongqing Cheng, Jinxin Xue

Jazyk:

Väzba: Pevná

Vydavateľ: Springer, Berlin

Dostupnosť: 50 % šanca

Prehľadáme celý svet

164.23 €

This book presents the advanced theory of Hamiltonian dynamics, with an emphasis on the recent devel...

Informácie o knihe

Autor

Chongqing Cheng, Jinxin Xue

Jazyk

Angličtina

Väzba

Kniha - Pevná

Vydalo

2026

Stránok

460

EAN

9789819559640

Enbook ID

50033305

Vydavateľ

Springer, Berlin

Rozmery

155 x 235

Kompletný popis

This book presents the advanced theory of Hamiltonian dynamics, with an emphasis on the recent development of variational methods and its application to the problem of Arnold diffusion. The main theme of the book is to study the dynamics of finite dimensional nearly integrable Hamiltonian systems, which are small perturbations of integrable systems.

The book consists of two parts. Part I includes the main techniques in Hamiltonian dynamics such as the normal form theory (KAM theory, Nekhoroshev theorem), the hyperbolicity theory (the theorem of normally hyperbolic invariant manifold), the variational theory, systems of two degrees of freedom and the connecting orbit theory. In the more advanced Part II, authors specialized to Arnold diffusion. The techniques in Part I are fully exploited in Part II for people to understand theorems better via applications.The proof the classical Tonelli theorem, some preliminaries of ergodic theory and some basics of genercitity and transversality are given in the Appendix.

This book can be used as the textbook for graduate students in the field of Hamiltonian dynamics. It can also be used as reference for working mathematicians. Before reading this book, obtaining some understanding on Arnold's book Mathematical Methods in Classical Mechanics, algebraic topology, differential topology and convex analysis will be helpful.