%0 Journal Article
%T Nontrivial attractor-repellor maps of $S^2$ and rotation numbers
%A Shigenori Matsumoto
%J Mathematics
%D 2013
%I arXiv
%X We consider an orientation preserving homeomorphism $h$ of $S^2$ which admits a repellor denoted $\infty$ and an attractor $-\infty$, which is not a North-South map, such that the basins of $\infty$ and $-\infty$ intersect. We study various aspects of the rotation number of $h:S^2\setminus\{\pm\infty\}\to S^2\setminus\{\pm\infty\}$, especially its relationship with the existence of periodic orbits.
%U http://arxiv.org/abs/1302.4041v2