Rotation topological factors of minimal $\mathbb {Z}^{d}$-actions on the Cantor set
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- by Maria Isabel Cortez, Jean-Marc Gambaudo and Alejandro Maass PDF
- Trans. Amer. Math. Soc. 359 (2007), 2305-2315 Request permission
Abstract:
In this paper we study conditions under which a free minimal $\mathbb {Z}^d$-action on the Cantor set is a topological extension of the action of $d$ rotations, either on the product $\mathbb {T}^d$ of $d$ $1$-tori or on a single $1$-torus $\mathbb {T}^1$. We extend the notion of linearly recurrent systems defined for $\mathbb {Z}$-actions on the Cantor set to $\mathbb {Z}^d$-actions, and we derive in this more general setting a necessary and sufficient condition, which involves a natural combinatorial data associated with the action, allowing the existence of a rotation topological factor of one of these two types.References
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Additional Information
- Maria Isabel Cortez
- Affiliation: Departamento de Ingeniería Matemática, Fac. Ciencias Físicas y Matemáticas, Universidad de Chile, Av. Blanco Encalada 2120 5to piso, Santiago, Chile – and – Institut de Mathématiques de Bourgogne, U.M.R. CNRS 5584, Université de Bourgogne, U.F.R. des Sciences et Téchniques, B.P. 47870- 21078 Dijon Cedex, France
- Address at time of publication: Departamento de Matemática, Universidad de Santiago de Chile, Avenida Alameda Libertador O’Higgins 3363, Codigo Postal 7254758, Santiago, Chile
- Jean-Marc Gambaudo
- Affiliation: Centro de Modelamiento Matemático, U.M.R. CNRS 2071, Av. Blanco Encalada 2120, 7to piso, Santiago, Chile
- Address at time of publication: Université de Nice - Sophia Antipolis, Laboratoire J.-A. Dieudonné, UMR CNRS 6621, Parc Valrose, 06108 Nice cedex 2, France
- Alejandro Maass
- Affiliation: Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Fac. Ciencias Físicas y Matemáticas, Universidad de Chile, Av. Blanco Encalada 2120 5to piso, Santiago, Chile
- MR Author ID: 315077
- ORCID: 0000-0002-7038-4527
- Email: amaass@dim.uchile.cl
- Received by editor(s): August 25, 2004
- Received by editor(s) in revised form: March 24, 2005
- Published electronically: December 20, 2006
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 359 (2007), 2305-2315
- MSC (2000): Primary 54H20; Secondary 52C23
- DOI: https://doi.org/10.1090/S0002-9947-06-04027-X
- MathSciNet review: 2276621