6533b86ffe1ef96bd12cd1bf

RESEARCH PRODUCT

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

Alejandro MaassMaría Isabel CortezMaría Isabel CortezJ.-m. GambaudoJ.-m. Gambaudo

subject

Cantor setCombinatoricsApplied MathematicsGeneral MathematicsProduct (mathematics)TorusExtension (predicate logic)TopologyRotation (mathematics)Action (physics)Mathematics

description

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.

https://doi.org/10.1090/s0002-9947-06-04027-x