Nontrivial attractor-repellor maps of $S^2$ and rotation numbers

Shigenori Matsumoto

Nontrivial attractor-repellor maps of $S^2$ and rotation numbers

Dynamical Systems 2013-06-06 v2

Authors: Shigenori Matsumoto

Abstract

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.

Keywords

attractor-repellor maps orientation preserving homeomorphism rotation number periodic orbits North-South map

Cite

@article{arxiv.1302.4041,
  title  = {Nontrivial attractor-repellor maps of $S^2$ and rotation numbers},
  author = {Shigenori Matsumoto},
  journal= {arXiv preprint arXiv:1302.4041},
  year   = {2013}
}

Comments

24 pages, 6 figure

Related papers

View all related →