# Instability of pole singularities for the Chazy equation

@article{Kichenassamy1998InstabilityOP, title={Instability of pole singularities for the Chazy equation}, author={Satyanad Kichenassamy}, journal={Journal of Physics A}, year={1998}, volume={31}, pages={2675-2690} }

We prove that the negative resonances of the Chazy equation (in the sense of Painleve analysis) can be related directly to its group-invariance properties. These resonances indicate in this case the instability of pole singularities. Depending on the value of a parameter in the equation, an unstable isolated pole may turn into the familiar natural boundary, or split into several isolated singularities. In the first case, a convergent series representation involving exponentially small…

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