Rotation numbers for planar attractors of equivariant homeomorphisms

Abstract

Given an integer $m> 1$ we consider $\mathbb{Z}_m$-equivariant and orientation preserving homeomorphisms in $\mathbb{R}^2$ with an asymptotically stable fixed point at the origin. We present examples without periodic points and having some complicated dynamical features. The key is a preliminary construction of $\mathbb{Z}_m$-equivariant Denjoy maps of the circle.