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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 1998

Instability of pole singularities for the Chazy equation

Résumé

We prove that the negative resonances of the Chazy equation (in the sense of Painlev\'e 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 corrections can be given. This reconciles several earlier approaches to the interpretation of negative resonances. On the other hand, we also prove that pole singularities with the maximum number of positive resonances are stable. The proofs rely on general properties of nonlinear Fuchsian equations.
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Dates et versions

hal-00002646 , version 1 (28-04-2022)

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Satyanad Kichenassamy. Instability of pole singularities for the Chazy equation. Journal of Physics A: Mathematical and Theoretical, 1998, 31, pp.2675-2690. ⟨10.1088/0305-4470/31/11/015⟩. ⟨hal-00002646⟩
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