This article is cited in 13 papers

Brief communications

An Analytic Proof of the Nonintegrability of the ABC-flow for $A=B=C$

S. L. Ziglin

Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences

Abstract: 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, monodromy group, fundamental group.

UDC: 517.913

Received: 01.10.2001

DOI: 10.4213/faa160

 English version: Functional Analysis and Its Applications, 2003, 37:3, 225–227

Bibliographic databases:

• 
• 
• 
• 
•