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On the topological properties of symplectic maps

Published online by Cambridge University Press:  14 November 2011

H. Hofer
Affiliation:
Faculty and Institute for Mathematics, Ruhruniversität Bochum, Universitätsstrasse 150, 4630 Bochum, West Germany

Synopsis

In this paper we show that symplectic maps have surprising topological properties. In particular, we construct an interesting metric for the symplectic diffeomorphism groups, which is related, but not obviously, to the topological properties of symplectic maps and phase space geometry. We also prove a certain number of generalised symplectic fixed point theorems and give an application to a Hamiltonian system.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1990

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References

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