Physical description 
1 online resource. 
Series 
Lecture notes of the Unione Matematica Italiana ; 16 

Lecture notes of the Unione Matematica Italiana ; 16.


Springer English/International eBooks 2015  Full Set

Bibliography 
Includes bibliographical references. 
Contents 
Beginning  Notes on Differential Geometry  Symplectic Manifolds  Poisson brackets environment  Cauchy Problem for HJ equations  Calculus of Variations and Conjugate Points  Asymptotic Theory of Oscillating Integrals  LusternikSchnirelman and Morse  Finite Exact Reductions  Other instances  Bibliography. 
Summary 
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 systematic utilization of Lagrangian submanifolds and their MaslovHṟmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of HamiltonJacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct welldefined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincar'̌s last geometric theorem and the Arnol'd conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrḏinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects. 
Other author 
SpringerLink issuing body.

Subject 
Symplectic and contact topology.


Electronic books. 
ISBN 
9783319110264 

3319110268 

9783319110257 

331911025X 
Standard Number 
10.1007/9783319110264 
