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Funktsional. Anal. i Prilozhen., 2003, Volume 37, Issue 3, Pages 77–80 (Mi faa160)  

This article is cited in 10 scientific papers (total in 10 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

DOI: https://doi.org/10.4213/faa160

Full text: PDF file (130 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.913
Received: 01.10.2001

Citation: S. L. Ziglin, “An Analytic Proof of the Nonintegrability of the ABC-flow for $A=B=C$”, Funktsional. Anal. i Prilozhen., 37:3 (2003), 77–80; Funct. Anal. Appl., 37:3 (2003), 225–227

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Haas F., “Jacobi structures in $\mathbb R^3$”, J. Math. Phys., 46:10 (2005), 102703, 11 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Przybylska M., “Differential Galois obstructions for integrability of homogeneous Newton equations”, J. Math. Phys., 49:2 (2008), 022701, 40 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Basu P., Zayas L.A.P., “Analytic nonintegrability in string theory”, Phys Rev D, 84:4 (2011), 046006  crossref  mathscinet  adsnasa  isi  elib  scopus
    4. Llibre J., Valls C., “A note on the first integrals of the ABC system”, J Math Phys, 53:2 (2012), 023505  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Basu P. Das D. Ghosh A. Zayas L.A.P., “Chaos Around Holographic Regge Trajectories”, J. High Energy Phys., 2012, no. 5, 077  crossref  mathscinet  zmath  isi  elib  scopus
    6. Tsygvintsev A., “Bounded Analytic Maps, Wall Fractions and Abc-Flow”, J. Approx. Theory, 174 (2013), 206–219  crossref  mathscinet  zmath  isi  elib  scopus
    7. Giataganas D. Zayas L.A.P. Zoubos K., “On Marginal Deformations and Non-Integrability”, J. High Energy Phys., 2014, no. 1, 129  crossref  isi  elib  scopus
    8. Huang K., Shi Sh., Li W., “Meromorphic Non-Integrability of Several 3D Dynamical Systems”, Entropy, 19:5 (2017), 211  crossref  mathscinet  isi  scopus
    9. Didov A.A., Uleysky M.Yu., “Analysis of Stationary Points and Their Bifurcations in the Abc-Flow”, Appl. Math. Comput., 330 (2018), 56–64  crossref  mathscinet  isi  scopus
    10. Szuminski W., “On Certain Integrable and Superintegrable Weight-Homogeneous Hamiltonian Systems”, Commun. Nonlinear Sci. Numer. Simul., 67 (2019), 600–616  crossref  mathscinet  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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