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Regular and Chaotic Dynamics, 2007, Volume 12, Issue 6, Pages 622–629
DOI: https://doi.org/10.1134/S1560354707060056 (Mi rcd643) 		 
This article is cited in 11 scientific papers (total in 11 papers)

On the 65th birthday of R.Cushman

Non-Integrability of Some Painlevé VI-Equations and Dilogarithms

E. Horozovab, T. Stoyanovaa

a Department of Mathematics and Informatics, Sofia University, 5 J. Bourchier Blvd., Sofia 1126, Bulgari
b Institute of Mathematics and Informatics, Bulg. Acad. of Sci., Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgari
Citations (11)
DOI: https://doi.org/10.1134/S1560354707060056
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.
Keywords: integrability, Painlevé VI-equations, Hamiltonian system.
Received: 12.08.2007
Accepted: 25.10.2007
Bibliographic databases:
Document Type: Personalia
MSC: 34M55, 37J30
Language: English
Citation: E. Horozov, T. Stoyanova, “Non-Integrability of Some Painlevé VI-Equations and Dilogarithms”, Regul. Chaotic Dyn., 12:6 (2007), 622–629
Citation in format AMSBIB
\Bibitem{HorSto07}
\by E.~Horozov, T. Stoyanova
\paper Non-Integrability of Some Painlev\'{e} VI-Equations and Dilogarithms
\jour Regul. Chaotic Dyn.
\yr 2007
\vol 12
\issue 6
\pages 622--629
\mathnet{http://mi.mathnet.ru/rcd643}
\crossref{https://doi.org/10.1134/S1560354707060056}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2373162}
\zmath{https://zbmath.org/?q=an:1229.37057}
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    • This publication is cited in the following 11 articles:
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