Let be an orientation preserving homeomorphism of which has a continuum as a minimal set. Then there are exactly two connected components of which are left invariant by 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 . Enseign. Math. 57 (2011), no. 3/4, pp. 373–392DOI 10.4171/LEM/57-3-5