# Continued Fractions and Generalizations with Many Limits: A Survey

## TL;DR

This survey reviews recent advances in understanding the behavior of various infinite processes like continued fractions and matrix products that diverge in predictable ways under certain conditions.

## Contribution

It compiles and discusses recent results on divergent infinite processes, highlighting new insights into their predictable divergence patterns.

## Key findings

- Identification of conditions leading to divergence
- Characterization of predictable divergence patterns
- Extension of classical convergence theories

## Abstract

There are infinite processes (matrix products, continued fractions, $(r,s)$-matrix continued fractions, recurrence sequences) which, under certain circumstances, do not converge but instead diverge in a very predictable way. We give a survey of results in this area, focusing on recent results of the authors.