An ergodic study of Painlevé VI

Katsunori Iwasaki; Takato Uehara

doi:10.1007/s00208-006-0077-8

An ergodic study of Painlevé VI

Katsunori Iwasaki, Takato Uehara

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

An ergodic study of Painlevé VI is developed. The chaotic nature of its Poincaré 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 Painlevé VI, a Riemann-Hilbert correspondence, the dynamical system of a birational map on a cubic surface, and the Lefschetz fixed point formula.

Original language	English
Pages (from-to)	295-345
Number of pages	51
Journal	Mathematische Annalen
Volume	338
Issue number	2
DOIs	https://doi.org/10.1007/s00208-006-0077-8
Publication status	Published - Jun 2007
Externally published	Yes

Keywords

Chaos
Entropy
Ergodic theory
Invariant measure
Painlevé VI

ASJC Scopus subject areas

Mathematics(all)

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