2005/12/27 by Iwasaki, Katsunori, Uehara, Takato
#34M55 #37F10 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.math/0512583
The number of periodic solutions to Painlevé VI along a Pochhammer loop is counted exactly. It is shown that the number grows exponentially with period, where the growth rate is determined explicitly. Principal ingredients of the computation are a moduli-theoretical formulation of Painlevé VI, a Riemann-Hilbert correspondence, the dynamical system of a birational map on a cubic surface, and the Lefschetz fixed point formula.