Instability of pole singularities for the Chazy equation

  title={Instability of pole singularities for the Chazy equation},
  author={Satyanad Kichenassamy},
  journal={Journal of Physics A},
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… 


In recent times singularity analysis has become an integral component of the standard approach to the analysis of differential equations, be they ordinary or par- tial, scalar or system. This

Stellar models and irregular singularities

This paper proves two results on the determination of asymptotics of solutions of linear and nonlinear ODE. The first shows the stability of singular solutions of the point-source model of stellar

Parameterizations of the Chazy Equation

The Chazy equation y‴= 2yy″− 3y′2 is derived from the automorphic properties of Schwarz triangle functions S(α, β, γ; z). It is shown that solutions y which are analytic in the fundamental domain of

Singularity analysis for autonomous and nonautonomous differential equations

Singularity analysis of ordinary differential equations is an important tool in the determination of the possible integrability of the equations. Although singularity analysis has been studied



Analysing negative resonances in the Painlevé test

Analytic and asymptotic methods for nonlinear singularity analysis: a review and extensions of tests for the Painlevé property

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is

Symmetry and the Chazy Equation

There are three different actions of the unimodular Lie group SL(2, C) on a two-dimensional space. In every case, we show how an ordinary differential equation admitting SL(2) as a symmetry group can

A Local Asymptotic Method of Seeing the Natural Barrier of the Solutions of the Chazy Equation

The Chazy equation is a third-order nonlinear ordinary differential equation whose solutions are known to have a movable natural barrier, i.e. a closed curve on the complex sphere whose location

Analytic description of singularities in Gowdy spacetimes

We use the Fuchsian algorithm to construct singular solutions of Einstein's equations which belong to the class of Gowdy spacetimes. The solutions have the maximum number of arbitrary functions.


We construct generalized Painleve expansions with logarithmic terms for a general class of ('non-integrable') scalar equations, and describe their structure in detail. These expansions were

The Painlevé property for partial differential equations

In this paper we define the Painleve property for partial differential equations and show how it determines, in a remarkably simple manner, the integrability, the Backlund transforms, the linearizing

The blow-up problem for exponential nonlinearities

We give a solution of below-up problem for equation , with data close to constans, in any number of spce dimensions: there exists a blow-up surface, near which the solution has logarithmic behavior;