Geometric Aspects of the Painlev\'e Equations ${\rm PIII(D_6)}$ and ${\rm PIII(D_7)}$

Jaap Top; Marius van der Put

arxiv: 1207.4023 · v3 · pith:7XWUKXEInew · submitted 2012-07-17 · 🧮 math.AG

Geometric Aspects of the Painlev\'e Equations {rm PIII(D₆)} and {rm PIII(D₇)}

Marius van der Put , Jaap Top This is my paper

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keywords piiiequationspainlevacklundapproachaspectsconnectionsdata

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The Riemann-Hilbert approach for the equations ${\rm PIII(D_6)}$ and ${\rm PIII(D_7)}$ is studied in detail, involving moduli spaces for connections and monodromy data, Okamoto-Painlev\'e varieties, the Painlev\'e property, special solutions and explicit B\"acklund transformations.

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Geometric Aspects of the Painlev\'e Equations {rm PIII(D₆)} and {rm PIII(D₇)}

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