Prime end rotation numbers of invariant separating continua of annular homeomorphisms (Q2880643)
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scientific article; zbMATH DE number 6024091
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Prime end rotation numbers of invariant separating continua of annular homeomorphisms |
scientific article; zbMATH DE number 6024091 |
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Prime end rotation numbers of invariant separating continua of annular homeomorphisms (English)
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13 April 2012
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continuum
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rotation set
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prime end rotation number
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Brower line
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foliations
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The author considers a homeomorphism of the closed annulus, isotopic to the identity. Let \(X\) be an invariant connected compact set separating the annulus into two connected invariant domains (upper and lower), each containing the corresponding boundary of the annulus. Fixing a lift to the universal cover of the the annulus, one defines a rotation set by means of the invariant measures on \(X\), as well as the prime end rotation numbers of the upper and lower domains. The author shows that these prime end rotation numbers belong to the rotation set, for any choice of \(X\).
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