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

研究成果: Article › 査読

16 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	295-345
ページ数	51
ジャーナル	Mathematische Annalen
巻	338
号	2
DOI	https://doi.org/10.1007/s00208-006-0077-8
出版ステータス	Published - 2007 6月
外部発表	はい

ASJC Scopus subject areas

数学一般

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10.1007/s00208-006-0077-8

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AB - 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.

KW - Chaos

KW - Entropy

KW - Ergodic theory

KW - Invariant measure

KW - Painlevé VI

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An ergodic study of Painlevé VI

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