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.
Introduces Hamiltonian dynamics from the very beginning, culminating in the most important recent results: Kolmogorov's and Nekhoroshev's.
Antonio Giorgilli is a retired Professor of Mathematics at the Universita degli Studi di Milano and has been elected corresponding member of Istituto Lombardo Accademia di Scienze e Lettere since 2005. He has taught courses in mathematical physics and dynamical systems ranging from undergraduate to PhD level. His research in dynamical systems focuses on the characterization of chaos, KAM theory and Nekhoroshev's theory on exponential stability. In addition to being an Invited Speaker of the 1998 International Congress of Mathematicians, Giorgilli's other notable honors include the International Gili Agostinelli Prize for Pure or Applied Mechanics or Classical Mathematical Physics by the Accademia delle Scienze di Torino in 2007. The minor planet 27855 Giorgilli, discovered in 1995, is named in his honor.
'The classical mechanics of systems of finitely many point
particles belongs to the bedrock of theoretical physics every
physicist has to be familiar with. Giorgilli's book on Hamiltonian
mechanics is a treasure chest. It conveys the author's profound
knowledge of the history of the subject and provides a pedagogical
exposition of the basic mathematical techniques. Very many
important examples of systems are discussed, and the reader is
guided towards fairly recent and new developments in this important
subject. This book will become a classic.' Jurg Froehlich, ETH
Zurich
'This is an impressive book by one of the protagonists of the
modern theory of dynamical systems. It contains the basic steps of
the Hamiltonian theory, but it emphasizes the modern developments
of the theory that started with Poincare and Birkhoff, reaching the
study of chaos. The book has two important advantages: it gives the
successive steps needed by a beginner who enters this field, up to
its most recent developments, and it provides a remarkable
historical account of the developments of the theory. Giorgilli
introduced many new ideas in the theory of dynamical systems, but
he presents the new developments in a systematic way without
emphasizing his own contributions. This book will be of great value
for anyone interested in dynamics, and it is absolutely necessary
for any library in Physics, Astronomy and related fields.' George
Contopoulos, Academy of Athens
'This is a book that the reader will refer to over and over again:
it provides a theoretical and practical framework for understanding
Hamiltonian formalism and classical perturbation theory. It
contains a readable complete proof of the most important results in
the field (Kolmogorov-Arnold-Moser theorem and Nekhoroshev's
theorem) as well as their applications to the fundamental problems
of celestial mechanics. It also explains how small divisors are at
the origin of the divergence of perturbation series and Poincare's
discovery of homoclinic intersections and of chaotic behavior in
near-to-integrable systems. What a remarkably useful and exciting
book!' Stefano Marmi, Scuola Normale Superiore, Pisa
'This amazing book, written by a prominent master of the theory of
Hamiltonian systems, is a wonderful gift for anyone interested in
Classical Dynamics, from a novice student to a sophisticated
expert. The author, together with the reader, goes from the
definition of canonical equations to such shining peaks as the
Kolmogorov theorem on invariant tori and the Nekhoroshev theorem on
exponential stability (with complete proofs, and for each of these
fundamental theorems two entirely different proofs are presented!).
Carefully selected examples and exercises and historical
digressions greatly facilitate learning the material and turn
reading the book into an intellectual festivity.' Mikhail Sevryuk,
Semenov Federal Research Center of Chemical Physics, Moscow
'Giorgilli builds up the whole architecture of Hamiltonian Dynamics
chapter by chapter in a delightful succession of ideas with many
examples. This book will certainly become an essential reference
for basic and for advanced courses and it will also be a source of
inspiration for experts in the field.' Angel Jorba, University of
Barcelona
'This book is an excellent and exhaustive treatise on Hamiltonian
systems aimed at both students and researchers, which collects in
great detail the classical results and contains a very accurate
description of the theory of perturbations. It is a reference book
on constructive methods, which are successfully applied throughout
the book in many examples, most notably those of Celestial
Mechanics.' Amadeu Delshams, BarcelonaTech
|
Ask a Question About this Product More... |
|
