Horocycle flows without minimal sets

TL;DR

This paper proves that horocycle flows on open tight hyperbolic surfaces lack minimal sets, providing new insights into their dynamical properties.

Contribution

It establishes the non-existence of minimal sets for horocycle flows on a specific class of hyperbolic surfaces, a novel result in dynamical systems.

Findings

Horocycle flows on open tight hyperbolic surfaces have no minimal sets.

The result advances understanding of the dynamics of horocycle flows.

Provides a new perspective on the structure of hyperbolic surface flows.

Abstract

We show that the horocycle flows of open tight hyperbolic surfaces do not admit minimal sets.