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Rotation Vectors and Fixed Points of Area Preserving Surface Diffeomorphisms
Author(s):
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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Additional Information:
John
Franks
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208-2730
Email:
john@math.nwu.edu
DOI:
10.1090/S0002-9947-96-01502-4
PII:
S 0002-9947(96)01502-4
Received by editor(s):
September 20, 1994
Received by editor(s) in revised form:
March 31, 1995
Copyright of article:
Copyright
1996,
American Mathematical Society
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