Some Geometric Evolution Equations Arising as Geodesic Equations on Groups of Diffeomorphisms Including the Hamiltonian Approach
نویسنده
چکیده
Introduction 1. A general setting and a motivating example 2. Weak symplectic manifolds 3. Right invariant weak Riemannian metrics on Lie groups 4. The Hamiltonian approach 5. Vanishing geodesic distance on groups of diffeomorphisms 6. The regular Lie group of rapidly decreasing diffeomorphisms 7. The diffeomorphism group of S or R, and Burgers’ hierarchy 8. The Virasoro-Bott group and the Korteweg-de Vries hierarchy Appendix A. Smooth Calculus beyond Banach spaces Appendix B. Regular infinite dimensional Lie groups References
منابع مشابه
Weak symplectic forms and differential calculus in Banach spaces
1Jerrold E. Marsden and Tudor S. Ratiu, Introduction to Mechanics and Symmetry, second ed., Chapter 2. 2Serge Lang, Differential and Riemannian Manifolds, p. 150, Theorem 8.1; Mircea Puta, Hamiltonian Mechanical Systems and Geometric Quantization, p. 12, Theorem 1.3.1. 3Andreas Kriegl and Peter W. Michor, The Convenient Setting of Global Analysis, p. 522, §48; Peter W. Michor, Some geometric ev...
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