An ergodic study of Painleve VI
Algebraic Geometry
2007-05-23 v1 Dynamical Systems
Abstract
An ergodic study of Painleve VI is developed. The chaotic nature of its Poincare return map is established for almost all loops. The exponential growth of the numbers of periodic solutions is also shown. Principal ingredients of the arguments are a moduli-theoretical formulation of Painleve VI, a Riemann-Hilbert correspondence, the dynamical system of a birational map on a cubic surface, and the Lefschetz fixed point formula.
Cite
@article{arxiv.math/0604582,
title = {An ergodic study of Painleve VI},
author = {Katsunori Iwasaki and Takato Uehara},
journal= {arXiv preprint arXiv:math/0604582},
year = {2007}
}
Comments
40 pages, 11 figures, 4 tables, 32 references, an upgraded version of the article: arXiv: math.AG/0512583