Mathematics – Algebraic Geometry
Scientific paper
2009-09-29
Mathematics
Algebraic Geometry
34 pages, 15 figures, 3 tables
Scientific paper
We develop a dynamical study of the sixth Painleve equation for all parameters generalizing an earlier work for generic parameters. Here the main focus of this paper is on non-generic parameters, for which the corresponding character variety becomes a cubic surface with simple singularities and the Riemann-Hilbert correspondence is a minimal resolution of the singular surface, not a biholomorphism as in the generic case. Introducing a suitable stratification on the parameter space and based on geometry of singular cubic surfaces, we establish a chaotic nature of the nonlinear monodromy map of Painleve VI and give a precise estimate for the number of its isolated periodic solutions.
Iwasaki Katsunori
Uehara Takato
No associations
LandOfFree
Singular cubic surfaces and the dynamics of Painleve VI does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Singular cubic surfaces and the dynamics of Painleve VI, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Singular cubic surfaces and the dynamics of Painleve VI will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-664615