JournalslemVol. 57, No. 3/4pp. 373–392

Continua as minimal sets of homeomorphisms of S2S^2

  • Shigenori Matsumoto

    Nihon University of Science and Technology, Tokyo, Japan
  • Hiromichi Nakayama

    Aoyama Gakuin University, Kanagawa, Japan
Continua as minimal sets of homeomorphisms of $S^2$ cover
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Abstract

Let ff be an orientation preserving homeomorphism of S2S^2 which has a continuum XX as a minimal set. Then there are exactly two connected components of S2XS^2\setminus X which are left invariant by ff and all the others are wandering. The Carathéodory rotation number of an invariant component is irrational.

Cite this article

Shigenori Matsumoto, Hiromichi Nakayama, Continua as minimal sets of homeomorphisms of S2S^2. Enseign. Math. 57 (2011), no. 3, pp. 373–392

DOI 10.4171/LEM/57-3-5