A symplectic fixed point theorem on open manifolds
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- by Michael Colvin and Kent Morrison PDF
- Proc. Amer. Math. Soc. 84 (1982), 601-604 Request permission
Abstract:
In 1968 Bourgin proved that every measure-preserving, orientation-preserving homeomorphism of the open disk has a fixed point, and he asked whether such a result held in higher dimensions. Asimov, in 1976, constructed counterexamples in all higher dimensions. In this paper we answer a weakened form of Bourgin’s question dealing with symplectic diffeomorphisms: every symplectic diffeomorphism of an even-dimensional cell sufficiently close to the identity in the ${C^1}$-fine topology has a fixed point. This result follows from a more general result on open manifolds and symplectic diffeomorphisms.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 601-604
- MSC: Primary 58C30; Secondary 55M20, 57S99, 58D05, 58F10
- DOI: https://doi.org/10.1090/S0002-9939-1982-0643757-6
- MathSciNet review: 643757