Elementary Symplectic Topology and Mechanics

• Main Author: Cardin, Franco (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Series: Lecture Notes of the Unione Matematica Italiana, 16
• Subjects: Mathematics.; Differential geometry.; Calculus of variations.; Mathematical physics.; Mathematical Physics.; Differential Geometry.; Calculus of Variations and Optimal Control; Optimization.

This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the...

Table of Contents:

• Beginning
• Notes on Differential Geometry
• Symplectic Manifolds
• Poisson brackets environment
• Cauchy Problem for H-J equations
• Calculus of Variations and Conjugate Points
• Asymptotic Theory of Oscillating Integrals
• Lusternik-Schnirelman and Morse
• Finite Exact Reductions
• Other instances
• Bibliography.