Elementary Symplectic Topology and Mechanics

Nonfiction, Science & Nature, Mathematics, Geometry, Science, Physics, Mathematical Physics
Cover of the book Elementary Symplectic Topology and Mechanics by Franco Cardin, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Franco Cardin ISBN: 9783319110264
Publisher: Springer International Publishing Publication: December 1, 2014
Imprint: Springer Language: English
Author: Franco Cardin
ISBN: 9783319110264
Publisher: Springer International Publishing
Publication: December 1, 2014
Imprint: Springer
Language: English

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 Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined 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 Poincaré'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 Schrödinger 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined 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 Poincaré'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 Schrödinger 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.

More books from Springer International Publishing

Cover of the book Memory Frictions in Contemporary Literature by Franco Cardin
Cover of the book Intelligent Medical Decision Support System Based on Imperfect Information by Franco Cardin
Cover of the book Molecularly Imprinted Polymers in Biotechnology by Franco Cardin
Cover of the book Economics of the Anthropocene Age by Franco Cardin
Cover of the book Insecurity, Precarious Work and Labour Markets by Franco Cardin
Cover of the book Effective Evolution Equations from Quantum Dynamics by Franco Cardin
Cover of the book Genetic Resources of Neotropical Fishes by Franco Cardin
Cover of the book Europe and the End of the Age of Innocence by Franco Cardin
Cover of the book Models of Thermochemical Heat Storage by Franco Cardin
Cover of the book 3D Automated Breast Volume Sonography by Franco Cardin
Cover of the book Languages, Design Methods, and Tools for Electronic System Design by Franco Cardin
Cover of the book Nanoporous Alumina by Franco Cardin
Cover of the book The British Role in Iranian Domestic Politics (1951-1953) by Franco Cardin
Cover of the book Large Deviations and Asymptotic Methods in Finance by Franco Cardin
Cover of the book A Clinician's Guide to Pemphigus Vulgaris by Franco Cardin
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy