Removing index $0$ fixed points for area preserving maps of two-manifolds
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- by Edward E. Slaminka PDF
- Trans. Amer. Math. Soc. 340 (1993), 429-445 Request permission
Abstract:
Using the method of free modifications developed by M. Brown and extended to area preserving homeomorphisms, we prove the following fixed point removal theorem. Theorem. Let $h:M \to M$ be an orientation preserving, area preserving homeomorphism of an orientable two-manifold $M$ having an isolated fixed point $p$ of index $0$. Given any open neighborhood $N$ of $p$ such that $N \cap \operatorname {Fix}(h) = p$, there exists an area preserving homeomorphism $\hat h$ such that (i) \[ \hat h = h\;on\;\overline {M - N} \] and (ii) $\hat h$ is fixed point free on $N$. Two applications of this theorem are the second fixed point for the topological version of the Conley-Zehnder theorem on the two-torus, and a new proof of the second fixed point for the Poincaré-Birkhoff Fixed Point Theorem.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 340 (1993), 429-445
- MSC: Primary 58F20; Secondary 54H20, 58F10
- DOI: https://doi.org/10.1090/S0002-9947-1993-1145963-5
- MathSciNet review: 1145963