On some properties of focal points (Q1040154)

In continuation to their work [Discrete Dyn. Nat. Soc. 2005, No.~3, 343--355 (2005; Zbl 1137.37021)], the authors study dynamical properties of two dimensional maps having an inverse with vanishing denominator. A prefocal curve of a map is a set of points whose image by one inverse is reduced into a single point called a focal point. The authors discuss facts regarding the role of focal points and prefocal curves. Further, they investigate necessary and/or sufficient conditions for a focal point to be a fixed point of the inverse map. Finally, applications are discssed by considering two examples with one focal point and two focal points.