# Effective equidistribution of the horocycle flow on geometrically finite hyperbolic surfaces

## TL;DR

This paper proves that non-closed horocycles distribute evenly over infinite-volume hyperbolic surfaces, providing effective rates of equidistribution in the unit tangent bundle.

## Contribution

It establishes effective equidistribution results for non-closed horocycles on geometrically finite hyperbolic surfaces, extending previous work to infinite-volume cases.

## Key findings

- Effective equidistribution rates are obtained.
- Results apply to infinite-volume geometrically finite hyperbolic surfaces.
- Advances understanding of horocycle dynamics in non-compact settings.

## Abstract

We prove effective equidistribution of non-closed horocycles in the unit tangent bundle of infinite-volume geometrically finite hyperbolic surfaces.