Typical recurrence for the ehrenfest wind-tree model

TL;DR

This paper proves that the typical wind-tree model and Lorentz gas are recurrent and have dense periodic orbits, even without finite horizon, advancing understanding of their long-term dynamical behavior.

Contribution

It establishes recurrence and density of periodic orbits for typical wind-tree models and Lorentz gases in the Baire sense, including cases without finite horizon.

Findings

Typical wind-tree models are recurrent and have dense periodic orbits.

The recurrence property extends to the Lorentz gas, even with infinite horizon.

These results hold in the Baire category sense, indicating generic behavior.

Abstract

We show that the typical wind-tree model, in the sense of Baire, is recurrent and has a dense set of periodic orbits. The recurrence result also holds for the Lorentz gas : the typical Lorentz gas, in the sense of Baire, is recurrent. These Lorentz gases need not be of finite horizon!