Critical behaviours of the fifth Painlevé transcendents and the monodromy data

Shun Shimomura

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

For the fifth Painlevé equation, we present families of convergent series solutions near the origin and the corresponding monodromy data for the associated isomonodromy linear system. These solutions are of complex power type, of inverse logarithmic type and of Taylor series type. For generic parameters the total set of these critical behaviours is almost complete. For the complex power type of solutions in the generic case, we clarify the structure of the analytic continuation on the universal covering around the origin, and examine the distribution of zeros, poles and 1-points. It is shown that two kinds of spiral domains including a sector as a special case are alternately arrayed; the domains of one kind contain sequences both of zeros and of poles, and those of the other kind sequences of 1-points.

Original languageEnglish
Pages (from-to)139-185
Number of pages47
JournalKyushu Journal of Mathematics
Volume71
Issue number1
DOIs
Publication statusPublished - 2017

Fingerprint

Monodromy
Critical Behavior
Pole
Distribution of Zeros
Analytic Continuation
Taylor series
Series Solution
Logarithmic
Sector
Covering
Linear Systems
Zero
Family

Keywords

  • Critical behaviour
  • Fifth Painlevé equation
  • Isomonodromy deformation
  • Monodromy data
  • Schlesinger equation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Critical behaviours of the fifth Painlevé transcendents and the monodromy data. / Shimomura, Shun.

In: Kyushu Journal of Mathematics, Vol. 71, No. 1, 2017, p. 139-185.

Research output: Contribution to journalArticle

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