We study the global analytic properties of the solutions of a particular family of Painleve' VI equations with the parameters β=γ=0, δ=12 and α arbitrary. We introduce a class of solutions having critical behaviour of algebraic type, and completely compute the structure of the analytic continuation of these solutions in terms of an auxiliary reflection group in the three dimensional space. The analytic continuation is given in terms of an action of the braid group on the triples of generators of the reflection group. This result is used to classify all the algebraic solutions of our Painleve' VI equation

Monodromy of certain Painleve`-VI transcendents and reflection groups / Dubrovin, Boris; Mazzocco, M.. - In: INVENTIONES MATHEMATICAE. - ISSN 0020-9910. - 141:1(2000), pp. 55-147. [10.1007/PL00005790]

Monodromy of certain Painleve`-VI transcendents and reflection groups

Dubrovin, Boris;
2000-01-01

Abstract

We study the global analytic properties of the solutions of a particular family of Painleve' VI equations with the parameters β=γ=0, δ=12 and α arbitrary. We introduce a class of solutions having critical behaviour of algebraic type, and completely compute the structure of the analytic continuation of these solutions in terms of an auxiliary reflection group in the three dimensional space. The analytic continuation is given in terms of an action of the braid group on the triples of generators of the reflection group. This result is used to classify all the algebraic solutions of our Painleve' VI equation
2000
141
1
55
147
https://link.springer.com/article/10.1007%2FPL00005790
https://arxiv.org/abs/math/9806056
Dubrovin, Boris; Mazzocco, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/17270
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