Geometric Mechanics and Symmetry
The Peyresq Lectures

The lectures in this 2005 book are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems.

James Montaldi (Edited by), Tudor Ratiu (Edited by)

9780521539579, Cambridge University Press

Paperback, published 5 May 2005

414 pages, 42 b/w illus. 2 colour illus.
22.9 x 15.2 x 2.3 cm, 0.6 kg

The lectures in this 2005 book are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems. They succinctly cover an unparalleled range of topics from the basic concepts of symplectic and Poisson geometry, through integrable systems, KAM theory, fluid dynamics, and symmetric bifurcation theory. The lectures are based on summer schools for graduate students and postdocs and provide complementary and contrasting viewpoints of key topics: the authors cut through an overwhelming amount of literature to show young mathematicians how to get to the core of the various subjects and thereby enable them to embark on research careers.

1. Stability in Hamiltonian systems: applications to the restricted three-body problem K. R. Meyer, B. Rink and T. Tuwankotta
2. A crash course in geometric mechanics T. S. Ratiu, E. Sousa Dias, L. Sbano, G. Terra and R. Tudoran
3. The Euler-Poincaré variational framework for modeling fluid dynamics D. D. Holm
4. No polar coordinates R. H. Cushman, D. Sadovskii and K. Efstanthiou
5. Survey on dissipative KAM theory including quasi-periodic bifurcation theory H. Broer, M.-C. Ciocci and A. Litvak-Hinenzon
6. Symmetric Hamiltonian bifurcations P.-L. Buono, F. Laurent-Polz and J. Montaldi.

Subject Areas: Nonlinear science [PBWR], Geometry [PBM], Functional analysis & transforms [PBKF], Real analysis, real variables [PBKB]