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Painleve Test and the Resolution of Singularities for Integrable Equations
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We prove that under a very general setting, a system of ODE passes the Painleve test if and only if there is a good change of variable, such that the pole singularity solutions are converted to regular power series, while the converted ODE system is still kept regular. A consequence is that all principal balances of an ODE system converge. We also prove that the results are natural with respect to Hamiltonian systems.
Forward citations
Cited by 2 Pith papers
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On the degeneration of Kovalevskaya exponents of Laurent series solutions of quasi-homogeneous vector fields
A commuting vector field turns a principal Laurent-series family of a quasi-homogeneous system into a lower one, with Kovalevskaya exponents given by the reduced free-parameter flow.
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Quasi-Homogeneous Integrable Systems: Free Parameters, Kovalevskaya Exponents, and the Painlev\'e Property
The paper's central resonance condition on Kovalevskaya exponents rests on a false combinatorial lemma, and its Frobenius manifold and symplectic pairing theorems contain unproved or internally inconsistent steps.
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