Some extensions of the Poincaré-Birkhoff theorem (Q395462)

In this work the authors present results on the existence of one and two fixed points for continuous maps or continuously differentiable maps of the annulus which are not area preserving and are not homeomorphic. Also they generalize the twist condition introducing the \((*)\)-condition which requires the existence of two points rotating in opposite angular directions in the annulus and prove the existence of two fixed points for a continuous \((*)\)-bend map satisfying some additional conditions. Finally the authors replace the bend condition by one concerning the critical points of the radial displacement \(I\) to describe the fixed point set for continuously differentiable maps.