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A Minimal Positive Entropy Homeomorphism of the 2-Torus

✍ Scribed by Rees, M.


Book ID
120095080
Publisher
Oxford University Press
Year
1981
Tongue
English
Weight
291 KB
Volume
s2-23
Category
Article
ISSN
0024-6107

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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