%0 Journal Article
%T Arcs, balls and spheres that cannot be attractors in $\mathbb{R}^3$
%A J. J. S¨˘nchez-Gabites
%J Mathematics
%D 2014
%I arXiv
%X For any compact set $K \subseteq \mathbb{R}^3$ we define a number $r(K)$ that is either a nonnegative integer or $\infty$. Intuitively, $r(K)$ provides some information on how wildly $K$ sits in $\mathbb{R}^3$. We show that attractors for discrete or continuous dynamical systems have finite $r$ and then prove that certain arcs, balls and spheres cannot be attractors by showing that their $r$ is infinite.
%U http://arxiv.org/abs/1406.5482v1