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Rotation Vectors and Fixed Points of Area Preserving Surface Diffeomorphisms


Author: John Franks
Journal: Trans. Amer. Math. Soc. 348 (1996), 2637-2662
MSC (1991): Primary 58C30; Secondary 58F11
DOI: https://doi.org/10.1090/S0002-9947-96-01502-4
MathSciNet review: 1325916
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Abstract: We consider the (homological) rotation vectors for area preserving diffeomorphisms of compact surfaces which are homotopic to the identity. There are two main results. The first is that if $0$ is in the interior of the convex hull of the rotation vectors for such a diffeomorphism then $f$ has a fixed point of positive index. The second result asserts that if $f$ has a vanishing mean rotation vector then $f$ has a fixed point of positive index. There are several applications including a new proof of the Arnold conjecture for area preserving diffeomorphisms of compact surfaces.


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Additional Information

John Franks
Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208-2730
Email: john@math.nwu.edu

DOI: https://doi.org/10.1090/S0002-9947-96-01502-4
Received by editor(s): September 20, 1994
Received by editor(s) in revised form: March 31, 1995
Article copyright: © Copyright 1996 American Mathematical Society

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