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arXiv · 1302.4041

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

Shigenori Matsumoto
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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.

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Shigenori Matsumoto. 2013-02-17. Nontrivial attractor-repellor maps of $S^2$ and rotation numbers. https://arxiv.org/abs/1302.4041

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