  We analyse the automorphisms of solutions to Chazy's equation and the
generalised Chazy equation for the parameters $k=2,3,4$ and $9$. These
automorphisms are induced by triangular domains with isosceles symmetry. We
also prove theorems about the transformations of solutions to the generalised
Chazy equation between various different parameters. Using the transformation
of solutions between parameters $k=2$ and $k=\frac{2}{3}$, we are able to prove
a result about the automorphism of the solutions to the $k=\frac{2}{3}$
generalised Chazy equation.

Classical Analysis and ODEs