@article{Chakravarty2025, 
author = {S. Chakravarty and P. Guha},
title = {The DH5 system and the Chazy and Ramamani equations},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {6318-6337},
keywords = {Darboux-Halphen, Chazy, Ramamani, Schwarzian, automorphic functions, hypergeometric},
url = {https://www.sciopen.com/article/10.3934/math.2025288},
doi = {10.3934/math.2025288},
abstract = {This article considers a class of nonlinear ordinary differential equations (ODEs) whose general solutions possess a natural boundary in the complex plane and admit special solutions that are automorphic under the action of subgroups of the modular group P       SL    2    (      Z    ). Specifically, a    3  ×  3 matrix valued system known as the Darboux-Halphen 9 (DH9) system and its fifth-order reduction to the DH5 system are discussed. These systems arise as reductions of the self-dual Yang-Mills equations of mathematical physics. It is shown that the equations discovered by J. Chazy (1908) and V. Ramamani (1970) are embedded in the DH5 system.}
}