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On the topological properties of symplectic maps

Published online by Cambridge University Press:  14 November 2011

H. Hofer
H. Hofer
Affiliation:
Faculty and Institute for Mathematics, Ruhruniversität Bochum, Universitätsstrasse 150, 4630 Bochum, West Germany
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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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 115 , Issue 1-2 , 1990 , pp. 25 - 38
Copyright
Copyright © Royal Society of Edinburgh 1990

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References

1Eliashberg, Y.. A theorem on the structure of wave fronts and its application in symplectic topology (preprint).Google Scholar
2Eliashberg, Y. and Hofer, H.. Towards the definition of a symplectic boundary (in preparation).Google Scholar
3Ekeland, I. and Hofer, H.. Symplectic topology and hamiltonian dynamics. Math. Zeit. 200 (1989), 355–378.CrossRefGoogle Scholar
4Ekeland, I. and Hofer, H.. Symplectic topology and hamiltonian dynamics II. Math. Z. (to appear 1990).CrossRefGoogle Scholar
5Ekeland, I. and Hofer, H.. Two symplectic fixed point theorems (to appear).Google Scholar
6Floer, A. and Hofer, H.. Instanton homology and symplectic capacities (in preparation).Google Scholar
7Gromov, M.. Pseudoholomorphic curves in symplectic manifolds. Invent. Math. 82 (1985), 307–347.CrossRefGoogle Scholar
8Hofer, H. and Zehnder, E.. Periodic solutions on hypersurfaces and a result by C. Viterbo. Invent. Math. 90 (1987), 1–9.CrossRefGoogle Scholar
9Hofer, H. and Zehnder, E.. A new capacity for symplectic manifolds, In Analysis, et cetera, ed. Rabinowitz, P. & Zehnder, E.. (New York: Academic Press, 1990.)Google Scholar
10Moser, J.. A fixed point problem in symplectic Geometry. Acta Math. 141 (1978), 17–34.CrossRefGoogle Scholar
11Viterbo, C.. A proof of the Weinstein conjecture, in ℝ2n. Ann. Inst. H. Poincaré, Anal. Non Linéaire 4 (1987), 337–357.CrossRefGoogle Scholar