The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology. Surprising rigidity phenomena demonstrate that the nature of symplectic mappings is very different from that of volume preserving mappings. Thisraises new questions, many of them still unanswered. On the other hand, analysis of an old variational principle in classical mechanics has established global periodic phenomena in Hamiltonian systems. As it turns out, these seemingly different phenomena are mysteriously related. One of the links is a class ofsymplectic invariants, called symplectic capacities. These invariants are themain theme of this book, which includes such topics as basic symplectic geometry, symplectic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a bi-invariant metric on the symplectic diffeomorphism group and its geometry, symplectic fixed point theory, the Arnold conjectures and first order elliptic systems, and finally a survey on Floer homologyand symplectic homology. The exposition is self-contained and addressed to researchers and students from the graduate level onwards. Opened new perspectives for the old field of Hamiltonian systems and let to the creation of a new field: symplectic topology. Invariants which grew out of lectures given by the authors. Selection by a single principle: the action principle of mechanics. INDICE: 1 Introduction. 2 Symplectic capacities. 3 Existence of a capacity. 4 Existence of closed characteristics. 5 Compactly supported symplectic mappings in R2n. 6 The Arnold conjecture, Floer homology and symplectic homology. Appendix. Index. Bibliography.
- ISBN: 978-3-0348-0103-4
- Editorial: Springer Basel
- Encuadernacion: Rústica
- Páginas: 341
- Fecha Publicación: 02/04/2011
- Nº Volúmenes: 1
- Idioma: Inglés