Recurrence in generic staircases

TL;DR

This paper demonstrates that the straight-line flow on most staircases and square tiled staircases is recurrent, with dense periodic orbits in the phase space for almost all square tiled staircases.

Contribution

It establishes recurrence and density of periodic orbits for straight-line flows on generic staircases and square tiled staircases, extending understanding of dynamical behavior in these structures.

Findings

Flow is recurrent on almost all staircases.

Periodic orbits are dense in phase space for almost all square tiled staircases.

Results apply to generic and square tiled staircase configurations.

Abstract

The straight-line flow on almost every staircase and on almost every square tiled staircase is recurrent. For almost every square tiled staircase the set of periodic orbits is dense in the phase space.