The star-shaped condition on Ding's version of the Poincaré-Birkhoff theorem

Abstract

W.-Y. Ding proved a generalization of the Poincaré–Birkhoff fixed point theorem not requiring that the boundary curves of the annular region be invariant circles. However, the inner boundary is assumed to be star-shaped with respect to the origin. We construct an example that shows that the star-shaped condition cannot be omitted without any replacement.