Introduction to Hamiltonian Dynamical Systems and the N-Body Problem

• Main Authors: Meyer, Kenneth (Author), Hall, Glen (Author), Offin, Dan (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Series: Applied Mathematical Sciences, 90
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Dynamics.; Ergodic theory.; Physics.; Dynamical Systems and Ergodic Theory.; Theoretical, Mathematical and Computational Physics.; Analysis.

This text grew out of graduate level courses in mathematics, engineering and physics given at several universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems...

Table of Contents:

• Hamiltonian Systems
• Equations of Celestial Mechanics
• Linear Hamiltonian Systems
• Topics in Linear Theory
• Exterior Algebra and Differential Forms
• Symplectic Transformations
• Special Coordinates
• Geometric Theory
• Continuation of Solutions
• Normal Forms
• Bifurcations of Periodic Orbits
• Variational Techniques
• Stability and KAM Theory
• Twist Maps and Invariant Circle.