2005/01/31 by Michi-aki Inaba, Katsunori Iwasaki, Masa-Hiko Saito · 1 citation
Mathematics · #math.AG #math.DS #msc:34M55 #msc:14D20 #msc:33E17 #msc:32G34 #msc:37J35
published as Séminaires et Congrès 14 (2006), Société Mathématique de France (SMF), 103--167 · 56 pages, 18 figures, reference updated
arxiv created 2005/03/06 · arxiv updated 2017/10/20
The sixth Painlevé equation is hiding extremely rich geometric structures behind its outward appearance. This article tries to give as a total picture as possible of its dynamical natures, based on the Riemann-Hilbert approach recently developed by the authors, using various techniques from algebraic geometry. A good part of the contents is extended to Garnier systems, while this article is restricted to the original sixth Painlevé equation.