# Discontinuous motions of limit sets

## TL;DR

This paper characterizes the conditions under which limit sets, described via Cannon-Thurston maps, change abruptly in the context of converging quasi-Fuchsian groups.

## Contribution

It provides a complete characterization of discontinuous motions of limit sets in algebraically convergent quasi-Fuchsian groups.

## Key findings

- Identifies criteria for discontinuous limit set motions
- Connects limit set behavior with algebraic convergence
- Enhances understanding of Cannon-Thurston maps

## Abstract

We characterise completely when limit sets, as parametrised by Cannon-Thurston maps, move discontinuously for a sequence of algebraically convergent quasi-Fuchsian groups.