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A new proof of the stable manifold theorem for hyperbolic fixed points on surfaces

โœ Scribed by Holland, Mark; Luzzatto, Stefano


Book ID
127356489
Publisher
Taylor and Francis Group
Year
2005
Tongue
English
Weight
223 KB
Volume
11
Category
Article
ISSN
1023-6198

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We give two combinatorial proofs of Franks' Theorem, that an area preserving torus homeomorphism with mean rotation zero has a fixed point. The first proof uses Lax's version of the Marriage Theorem. The second proof uses Euler's Theorem on circuits in graphs and an explicit method of Alpern for dec