Cubic and Quartic Transformations of the Sixth Painlevé Equation in Terms of Riemann–Hilbert Correspondence. Issue 1 (11th December 2012)

• Record Type: Journal Article
• Authors: Mazzocco, Marta; Vidunas, Raimundas
• Is Part Of: Studies in applied mathematics. Volume 130:Issue 1(2013)
• Page Start: 17
• Page End: 48
• Publication Date: 2012-12-11
• Subjects: Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/j.1467-9590.2012.00562.x
• Languages: English
• ISSNs: 0022-2526

Abstract

<abstract abstract-type="main" xml:lang="en"> <title> <x xml:space="preserve">Abstract</x> </title> <p>The starting point of this paper is a classification of quadratic polynomial transformations of the monodromy manifold for the 2 × 2 isomonodromic Fuchsian systems associated to the Painlevé VI equation. Up to birational automorphisms of the monodromy manifold, we find three transformations. Two of them are identified as the action of known quadratic or quartic transformations of the Painlevé VI equation. The third transformation of the monodromy manifold gives a new transformation of degree 3 of Picard's solutions of Painlevé VI.</p> </abstract>