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Fixed points of measure preserving torus homeomorphisms

โœ Scribed by Martin Flucher


Book ID
110558960
Publisher
Springer
Year
1990
Tongue
English
Weight
931 KB
Volume
68
Category
Article
ISSN
0025-2611

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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