By Helmut Hofer
The discoveries of the final many years have opened new views for the outdated box of Hamiltonian platforms and resulted in the production of a brand new box: symplectic topology. miraculous stress phenomena reveal that the character of symplectic mappings is particularly assorted from that of quantity protecting mappings. This increases new questions, lots of them nonetheless unanswered. nonetheless, research of an outdated variational precept in classical mechanics has validated worldwide periodic phenomena in Hamiltonian platforms. because it seems, those likely various phenomena are mysteriously comparable. one of many hyperlinks is a category of symplectic invariants, referred to as symplectic capacities. those invariants are the most subject of this e-book, consisting of such issues as uncomplicated symplectic geometry, symplectic capacities and stress, periodic orbits for Hamiltonian platforms and the motion precept, a bi-invariant metric at the symplectic diffeomorphism workforce and its geometry, symplectic mounted element concept, the Arnold conjectures and primary order elliptic platforms, and eventually a survey on Floer homology and symplectic homology.
The exposition is self-contained and addressed to researchers and scholars from the graduate point onwards.
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