New phenomena related to the presence of focal points in two-dimensional maps. (English) Zbl 0960.37019

This paper is devoted to dynamical properties of some class of 2D-maps, defined in the whole plane having focal points and prefocal sets. More precisely, the authors consider an invertible quadratic polynomial map of the plane whose inverse has a focal point, and it is shown how this fact can be used to explain some particular dynamical properties of the map. By an example they show that the iteration of such maps generates discrete dynamical systems with peculiar attracting sets, characterized by the presence of “knots” where infinitely many phase curves shrink into a single point.


37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
37E45 Rotation numbers and vectors
37C70 Attractors and repellers of smooth dynamical systems and their topological structure