Satyanad Kichenassamy 1998 J. Phys. A: Math. Gen. 31 2675 doi:10.1088/0305-4470/31/11/015
Satyanad Kichenassamy
Show affiliationsWe prove that the negative resonances of the Chazy equation (in the sense of Painlevé 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.
34M35 Singularities, monodromy, local behavior of solutions, normal forms
40A30 Convergence and divergence of series and sequences of functions
Issue 11 (20 March 1998)
Received 15 July 1997, in final form 18 November 1997
Satyanad Kichenassamy 1998 J. Phys. A: Math. Gen. 31 2675
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