# Four-Dimensional Painlev\'e-Type Equations Associated with Ramified Linear Equations III: Garnier Systems and Fuji-Suzuki Systems

## TL;DR

This paper completes a series on four-dimensional Painlevé-type equations by analyzing the degeneration of the Garnier and Fuji-Suzuki systems, contributing to the classification of these complex nonlinear equations.

## Contribution

It introduces the complete degeneration scheme for four-dimensional Painlevé-type equations, focusing on the Garnier and Fuji-Suzuki systems, advancing the understanding of their structure.

## Key findings

- Degeneration scheme of Garnier system in two variables elucidated
- Degeneration scheme of Fuji-Suzuki system analyzed
- Provides a comprehensive classification framework for these equations

## Abstract

This is the last part of a series of three papers entitled "Four-dimensional Painlev\'e-type equations associated with ramified linear equations". In this series of papers we aim to construct the complete degeneration scheme of four-dimensional Painlev\'e-type equations. In the present paper, we consider the degeneration of the Garnier system in two variables and the Fuji-Suzuki system.