Z^d-actions with prescribed topological and ergodic properties
Yuri Lima
TL;DR
This paper develops a method to construct Z^d-actions on symbolic spaces with specific topological and ergodic properties, including minimality, strict ergodicity, and positive entropy.
Contribution
It extends previous constructions to higher dimensions, enabling the creation of Z^d-actions with tailored dynamical and ergodic features.
Findings
Constructed Z^d-actions with prescribed properties
Achieved totally minimal and strictly ergodic actions
Demonstrated positive topological entropy in these systems
Abstract
We extend constructions of Hahn-Katznelson and Pavlov to Z^d-actions on symbolic dynamical spaces with prescribed topological and ergodic properties. More specifically, we describe a method to build Z^d-actions which are (totally) minimal, (totally) strictly ergodic and have positive topological entropy.
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