Continua as minimal sets of homeomorphisms of \(S^2\) (Q436517)
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scientific article; zbMATH DE number 6059290
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Continua as minimal sets of homeomorphisms of \(S^2\) |
scientific article; zbMATH DE number 6059290 |
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Continua as minimal sets of homeomorphisms of \(S^2\) (English)
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21 July 2012
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Summary: Let \(f\) be an orientation preserving homeomorphism of \(S^2\) which has a (nontrivial) continuum \(X\) as a minimal set. Then there are exactly two connected components of \(S^2\setminus X\) which are left invariant by \(f\) and all the others are wandering. The Carathéodory rotation number of an invariant component is irrational.
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orientation-preserving homeomorphism
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