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Non-integrability of some Painlevé VI-equations and dilogarithms

Non-integrability of some Painlevé VI-equations and dilogarithms The paper studies the Painlevé VIe equations from the point of view of Hamiltonian nonintegrability. For certain infinite number of points in the parameter space we prove that the equations are not integrable. Our approach uses recent advance in Hamiltonian integrability reducing the problem to higher differential Galois groups as well as the monodromy of dilogarithic functions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Non-integrability of some Painlevé VI-equations and dilogarithms

Regular and Chaotic Dynamics , Volume 12 (6) – Dec 18, 2007

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References (9)

Publisher
Springer Journals
Copyright
Copyright © 2007 by Pleiades Publishing, Ltd.
Subject
Mathematics; Dynamical Systems and Ergodic Theory
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354707060056
Publisher site
See Article on Publisher Site

Abstract

The paper studies the Painlevé VIe equations from the point of view of Hamiltonian nonintegrability. For certain infinite number of points in the parameter space we prove that the equations are not integrable. Our approach uses recent advance in Hamiltonian integrability reducing the problem to higher differential Galois groups as well as the monodromy of dilogarithic functions.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Dec 18, 2007

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