Nontrivial attractor-repellor maps of S² and rotation numbers

2013/02/17 by Shigenori Matsumoto, Matsumoto, Shigenori
Mathematics · Physics and Astronomy · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37E30

paper · pdf · doi:10.48550/arxiv.1302.4041

24 pages, 6 figure

arxiv created 2013/06/05 · arxiv updated 2013/06/06

Abstract

We consider an orientation preserving homeomorphism h of S² which admits a repellor denoted ∞ and an attractor -∞, which is not a North-South map, such that the basins of ∞ and -∞ intersect. We study various aspects of the rotation number of h:S²∖\±∞\→ S²∖\±∞\, especially its relationship with the existence of periodic orbits.

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