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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 181, Number 2, Pages 296–311
DOI: https://doi.org/10.4213/tmf8705 (Mi tmf8705) 		 
Nonintegrabilty of a Halphen system

J. Llibrea, C. Vallsb

a Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Catalonia, Spain
b Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisboa, Portugal
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DOI: https://doi.org/10.4213/tmf8705
Abstract: We study the Halphen system with real variables and real constants. We show that in the case where at least one constant is nonzero, this system does not admit any first integral that can be described by formal power series. It hence follows that analytic first integrals do not exist. Furthermore, we prove that first integrals of the Darboux type also do not exist.
Keywords: Halphen system, analytic first integral.
Received: 05.05.2014
English version:
Theoretical and Mathematical Physics, 2014, Volume 181, Issue 2, Pages 1383–1395
DOI: https://doi.org/10.1007/s11232-014-0219-1
Bibliographic databases:
MSC: 34C35, 34D30
Language: Russian
Citation: J. Llibre, C. Valls, “Nonintegrabilty of a Halphen system”, TMF, 181:2 (2014), 296–311; Theoret. and Math. Phys., 181:2 (2014), 1383–1395
Citation in format AMSBIB
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