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Rational ODEs with Movable Algebraic Singularities

Filipuk, G; Halburd, RG; (2009) Rational ODEs with Movable Algebraic Singularities. STUDIES IN APPLIED MATHEMATICS , 123 (1) 17 - 36.

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Abstract

A class of second-order rational ordinary differential equations, admitting certain families of formal algebraic series solutions, is considered. For all solutions of these equations, it is shown that any movable singularity that can be reached by analytic continuation along a finite-length curve is an algebraic branch point. The existence of these formal series expansions is straightforward to determine for any given equation in the class considered. We apply the theorem to a family of equations, admitting different kinds of algebraic singularities. As a further application we recover the known fact for generic values of parameters that the only movable singularities of solutions of the Painleve equations P-II-P-VI are poles.

Type: Article
Title: Rational ODEs with Movable Algebraic Singularities
Location: Beijing, PEOPLES R CHINA
Keywords: ORDINARY DIFFERENTIAL-EQUATIONS, LINEAR EVOLUTION-EQUATIONS, QUASI-PAINLEVE PROPERTY, DIRECT PROOF, P-TYPE, CONNECTION, IV
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: http://discovery.ucl.ac.uk/id/eprint/163661
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