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
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 is in the interior of the convex hull of the rotation vectors for such a diffeomorphism then has a fixed point of positive index. The second result asserts that if has a vanishing mean rotation vector then 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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Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208-2730
Received by editor(s): September 20, 1994
Received by editor(s) in revised form: March 31, 1995
Article copyright: © Copyright 1996 American Mathematical Society