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Rotation vectors and fixed points of area preserving surface diffeomorphisms. (English) Zbl 0862.58006
The author applies the machinery of homological rotation vectors (earlier developed by him) to the investigation of area preserving diffeomorphisms (homotopic to the identity) of compact surfaces. The main results are fixed point theorems for the above diffeomorphisms: A diffeomorphism \(f\) has a fixed point of positive index (i) if 0 is in the interior of the convex hull of rotation vectors of \(f\); (ii) if \(f\) has a vanishing mean rotation vector. Several applications of the theorems are given.

MSC:
58C30 Fixed-point theorems on manifolds
37A99 Ergodic theory
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