Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0960.34075
Dubrovin, B.; Mazzocco, M.
Monodromy of certain Painlevé-VI transcendents and reflection groups. (English)
[J] Invent. Math. 141, No.1, 55-147 (2000). ISSN 0020-9910; ISSN 1432-1297/e

This very extensive paper presents the particular case $\text{PVI}\mu$ of the Painlevé VI equation $\text{PVI}(\alpha, \beta,\mu,\delta)$, with $\alpha= {(2\mu- 1)^2\over 2}$, $\beta= \gamma=0$, $\delta={1\over 2}$. The single paragraphs of the paper are heading as follows:\par 1.1 Painlevé VI equation as isomonodromy deformation equation.\par 1.2 The structure of the analytic continuation.\par 1.3 Monodromy data and finite-branching solutions of the $\text{PVI}\mu$ equation.\par 1.4 Monodromy data and reflection groups.\par 2.0 Global structure of the solutions of Painlevé $\text{VI}\mu$ having critical behaviour of algebraic type.\par 2.1 Local theory of the solutions of $\text{PVI}\mu$ having critical behaviour of algebraic type.\par 2.2 The local asymptotic behaviour and the monodromy group of the Fuchsian system.\par 2.3 From the local asymptotic behaviour to the global one.\par 2.4 The complete list of algebraic solutions.
[Alois Klíč (Praha)]

MSC 2000:: *34M55 Painlevé and other special equations
34M35 Singularities, monodromy, local behavior of solutions, normal forms

Keywords: critical behaviour; reflection group; braid group; algebraic solutions; Puiseux series; monodromy

Cited in: Zbl 1172.20306 Zbl 1070.34123

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]