Finite branch solutions to Painleve VI around a fixed singular point

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dc.creatorIwasaki, Katsunori
dc.date2007-04-05
dc.date.accessioned2026-07-07T07:55:18Z
dc.date.available2026-07-07T07:55:18Z
dc.descriptionEvery finite branch solutions to the sixth Painleve equation around a fixed singular point is an algebraic branch solution. In particular a global solution is an algebraic solution if and only if it is finitely many-valued globally. The proof of this result relies on algebraic geometry of Painleve VI, Riemann-Hilbert correspondence, geometry and dynamics on cubic surfaces, resolutions of Kleinian singularities, and power geometry of algebraic differential equations. In the course of the proof we are also able to classify all finite branch solutions up to Backlund transformations.
dc.description45 pages, 22 figures, 5 tables
dc.identifierhttps://arxiv.org/abs/0704.0679
dc.identifierhttp://arxiv.org/abs/0704.0679
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126924
dc.subjectAlgebraic Geometry
dc.subjectClassical Analysis and ODEs
dc.subject34M55; 37F10
dc.titleFinite branch solutions to Painleve VI around a fixed singular point
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