Minimality of the Ehrenfest wind-tree model

TL;DR

This paper proves that in a generic class of wind-tree models, the dynamics are minimal in most directions and contain many periodic points, revealing fundamental properties of these aperiodic systems.

Contribution

It demonstrates that for a generic aperiodic wind-tree model, the dynamics are minimal in almost all directions and have dense periodic points, advancing understanding of these systems.

Findings

Dynamics are minimal in almost all directions.

Presence of a dense set of periodic points.

Results hold for a generic (Baire sense) configuration.

Abstract

We consider aperiodic wind-tree models, and show that for a generic (in the sense of Baire) configuration the wind-tree dynamics is minimal in almost all directions, and has a dense set of periodic points.