Geodesic
Nonintegrabilty of a~Halphen system
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 2, pp. 296-311

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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. 
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     author = {J. Llibre and C. Valls},
     title = {Nonintegrabilty of {a~Halphen} system},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {296--311},
     publisher = {mathdoc},
     volume = {181},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_181_2_a3/}
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J. Llibre; C. Valls. Nonintegrabilty of a~Halphen system. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 2, pp. 296-311. http://geodesic.mathdoc.fr/item/TMF_2014_181_2_a3/