### 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.

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.

#### Keywords

Planar embedding; symmetry; asymptotic stability; global attractors

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