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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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