Poncelet Polygons and the Painleve Equations

By N. Hitchin. 2004

87 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/debe43bd75071b631e5364d2e839913856bd68dc

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Citations in the corpus

Painlevé equations: nonlinear special functions (2003, methodology): “with κ and μ arbitrary constants, which was given by Hitchin [102].”
Katz's middle convolution algorithm (2006, background): “action on the moduli space look like? Some things to study in low-dimensional cases would be: compactifications [65] and their the dynamics [37] [38] [39] [12], the Hitchin system [70] [66], the relationship with Painlev´e equations [ 71 ] [14] [15] [47], jumps and wall-crossing phenomena such as in”
Classical Algebraic Geometry: A Modern View (2012, background): “The papers [398] and [299], [300] discuss the compactification of the variety of conjugate triangles.”
From Klein to Painlevé Via Fourier, Laplace and Jimbo (2003, methodology): “For example, there are the algebraic solutions of Hitchin [ 18 , 20], Dubrovin [11] and Dubrovin and Mazzocco [13] related to the dihedral, tetrahedral, octahedral and icosahedral groups.”
Positively curved cohomogeneity one manifolds and 3-Sasakian geometry (2005, background): “[ Hi2 ]. As a biproduct, the manifolds Pk and Qk all support 3-Sasakian Riemannian metrics, i.e., their Euclidean cones are Hyper-K¨ahler (see [BG] for a survey), and are in particular Einstein manifolds with positive scalar curvature.”
Topics in classical algebraic geometry (2006, background): “The papers of [202] and [156],[157] discuss the compactification of the variety of conjugate triangles.”
The Betti map associated to a section of an abelian scheme (2018, background): “Hitchin, and turned out to be related to the Painlevé VI equation [16] (see also work in progress by G.”