Fixed Point Theorem for Non-Self Maps of Regions in the Plane

Abstract

Let X and Y be compact, simply connected and locally connected subsets of R^2, and let f : X -> Y be a homeomorphism isotopic to the identity on X. Generalizing Brouwer's plane translation theorem for self-maps of the plane, we prove that f has no recurrent (in particular, no periodic) points if it has no fixed points.

arXiv comment11 pages, 5 figures; significant improvement and generalization of the result in the first version ("Jordan domains" replaced by "compact, simply connected, locally connected sets" in the assumptions of the main result)

References in corpus (1)

• Periodic orbits of period 3 in the disc