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 | References | Similar Articles | Additional Information

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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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