# A symplectic fixed point theorem on open manifolds

@inproceedings{Colvin1982ASF, title={A symplectic fixed point theorem on open manifolds}, author={Michael R. Colvin and Kent E. Morrison}, year={1982} }

In 1968 Bourgin proved that every measure-preserving, orientationpreserving 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'-fine topology has a fixed point…

## 3 Citations

### AREA-PRESERVING HOMEOMORPHISMS OF THE OPEN DISK WITHOUT FIXED POINTS

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D. G. Bourgin has proved that every measure-preserving orienta- tion-preserving homeomorphism of the open two-dimensional disk D has a fixed point. He suggested that the "result is perhaps valid even…

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We will show that measure-preserving transformations of Rn are recurrent if they satisfy a certain growth condition depending on the dimension n. Moreover, it is also shown that this condition is…

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