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

作者：Matsumoto Shigenori^*

来源：Journal of the Mathematical Society of Japan, 2015, 67(2): 477-501.

DOI：10.2969/jmsj/06720477

• attractor
• repellor
• prime ends
• rotation number

We consider an orientation preserving homeomorphism h of S-2 which admits a repellor denoted infinity and an attractor -infinity such that h is not a North-South map and that the basins of infinity and -infinity intersect. We study various aspects of the rotation number of h : S-2 \{+/-infinity} -> S-2 \ {+/-infinity}, especially its relationship with the existence of periodic orbits.

• 出版日期2015-4