Wandering intervals in affine extensions of self-similar interval exchange maps: The cubic Arnoux-Yoccoz map
Author
dc.contributor.author
Cobo, Milton
Author
dc.contributor.author
Gutiérrez Romo, Rodolfo Joaquín
Author
dc.contributor.author
Maass Sepúlveda, Alejandro
Admission date
dc.date.accessioned
2019-05-31T15:19:09Z
Available date
dc.date.available
2019-05-31T15:19:09Z
Publication date
dc.date.issued
2018
Cita de ítem
dc.identifier.citation
Ergodic Theory and Dynamical Systems, Volumen 38, Issue 7, 2018, Pages 2537-2570
Identifier
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14694417
Identifier
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01433857
Identifier
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10.1017/etds.2016.143
Identifier
dc.identifier.uri
https://repositorio.uchile.cl/handle/2250/169337
Abstract
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In this article, we provide sufficient conditions on a self-similar interval exchange map, whose renormalization matrix has complex eigenvalues of modulus greater than one, for the existence of affine interval exchange maps with wandering intervals that are semi-conjugate with it. These conditions are based on the algebraic properties of the complex eigenvalues and the complex fractals built from the natural substitution emerging from self-similarity. We show that the cubic Arnoux–Yoccoz interval exchange map satisfies these conditions.