Geodesic
An Analytic Proof of the Nonintegrability of the ABC-flow for $A=B=C$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 3, pp. 77-80

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We prove the absence of a real-analytic first integral in a known system describing the stationary flow of an ideal incompressible fluid with periodic boundary conditions and with velocity field collinear to the rotor of itself (an ABC-flow) for the case in which all three parameters occurring in the system are equal. A computer proof of this fact was previously known.
Keywords: ABC-flow, fundamental group.
Mots-clés : monodromy group 
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     title = {An {Analytic} {Proof} of the {Nonintegrability} of the {ABC-flow} for $A=B=C$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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S. L. Ziglin. An Analytic Proof of the Nonintegrability of the ABC-flow for $A=B=C$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 3, pp. 77-80. http://geodesic.mathdoc.fr/item/FAA_2003_37_3_a6/