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arXiv · 1306.0232

Fixed points for nilpotent actions on the plane and the Cartwright-Littlewood theorem

S. Firmo·J. Ribón·J. Velasco
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Abstract

The goal of this paper is proving the existence and then localizing global fixed points for nilpotent groups generated by homeomorphisms of the plane satisfying a certain Lipschitz condition. The condition is inspired in a classical result of Bonatti for commuting diffeomorphisms of the 2-sphere and in particular it is satisfied by diffeomorphisms, not necessarily of class $C^{1}$, whose linear part at every point is uniformly close to the identity. In this same setting we prove a version of the Cartwright-Littlewood theorem, obtaining fixed points in any continuum preserved by a nilpotent action.

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S. Firmo, J. Ribón, J. Velasco. 2013-06-02. Fixed points for nilpotent actions on the plane and the Cartwright-Littlewood theorem. https://doi.org/10.1007/s00209-014-1396-1

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