Attractors with vanishing rotation number

Abstract

Given an orientation-preserving homeomorphism of the plane, a rotation number can be associated with each locally attracting fixed point. Assuming that the homeomorphism is dissipative and the rotation number vanishes we prove the existence of a second fixed point. The main tools in the proof are Carathéodory prime ends and fixed point index. The result is applicable to some concrete problems in the theory of periodic differential equations.