An ergodic study of Painlevé VI

Katsunori Iwasaki, Takato Uehara

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)295-345
Number of pages51
JournalMathematische Annalen
Volume338
Issue number2
DOIs
Publication statusPublished - Jun 1 2007
Externally publishedYes

Fingerprint

Birational Maps
Cubic Surface
Return Map
Exponential Growth
Hilbert
Modulus
Periodic Solution
Correspondence
Dynamical system
Fixed point
Formulation

Keywords

  • Chaos
  • Entropy
  • Ergodic theory
  • Invariant measure
  • Painlevé VI

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

An ergodic study of Painlevé VI. / Iwasaki, Katsunori; Uehara, Takato.

In: Mathematische Annalen, Vol. 338, No. 2, 01.06.2007, p. 295-345.

Research output: Contribution to journalArticle

Iwasaki, Katsunori ; Uehara, Takato. / An ergodic study of Painlevé VI. In: Mathematische Annalen. 2007 ; Vol. 338, No. 2. pp. 295-345.
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