This text grew out of notes from a graduate course taught to students in mathematics and mechanical engineering. The goal was to take students who had somebasic knowledge of differential equations and lead them through a systematic grounding in the theory of Hamiltonian systems, an introduction to the theory of integrals and reduction. Poincaré’s continuation of periodic solution, normal forms, and applications of KAM theory. There is a special chapter devoted to the theory of twist maps and various extensions of the classic Poincaré-Birkhoff fixed point theorem. INDICE: Hamiltonian Differential Equations and the N-Body Problem.- Exterior Algebra and Differential Forms.- Symplectic transformations and coordinates.- Introduction to the Geometric Theory of Hamiltonian Dynamical Systems.- Continuation of Periodic Solutions.- Perturbation Theory and Normal Forms.- Bifurcations of Periodic Orbits.- Stability and KAM Theory.- Twist Maps and Invariant Curves.
- ISBN: 978-0-387-09723-7
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 350
- Fecha Publicación: 01/11/2008
- Nº Volúmenes: 1
- Idioma: Inglés