Rotation topological factors of minimal $\mathbb {Z}^{d}$-actions on the Cantor set

Autor:	Alejandro Maass, María Isabel Cortez, J.-M. Gambaudo
Rok vydání:	2006
Předmět:	Cantor set Combinatorics Applied Mathematics General Mathematics Product (mathematics) Torus Extension (predicate logic) Topology Rotation (mathematics) Action (physics) Mathematics
Zdroj:	Transactions of the American Mathematical Society. 359:2305-2315
ISSN:	1088-6850 0002-9947
DOI:	10.1090/s0002-9947-06-04027-x
Popis:	In this paper we study conditions under which a free minimal Z d -action on the Cantor set is a topological extension of the action of d rotations, either on the product T d of d 1-tori or on a single 1-torus T 1 . We extend the notion of linearly recurrent systems defined for Z-actions on the Cantor set to 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::dc38357a318b4eaf9c35f8487f0c1c6e https://doi.org/10.1090/s0002-9947-06-04027-x Zobrazit plný text záznamu