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Funktsional. Anal. i Prilozhen., 1996, Volume 30, Issue 2, Pages 80–81 (Mi faa525)  

This article is cited in 14 scientific papers (total in 14 papers)

Brief communications

The $ABC$-flow is not integrable for $A=B$

S. L. Ziglin

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

DOI: https://doi.org/10.4213/faa525

Full text: PDF file (209 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 1996, 30:2, 137–138

Bibliographic databases:

UDC: 517.913
Received: 23.03.1995

Citation: S. L. Ziglin, “The $ABC$-flow is not integrable for $A=B$”, Funktsional. Anal. i Prilozhen., 30:2 (1996), 80–81; Funct. Anal. Appl., 30:2 (1996), 137–138

Citation in format AMSBIB
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\by S.~L.~Ziglin
\paper The $ABC$-flow is not integrable for $A=B$
\jour Funktsional. Anal. i Prilozhen.
\yr 1996
\vol 30
\issue 2
\pages 80--81
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\zmath{https://zbmath.org/?q=an:0877.58050}
\transl
\jour Funct. Anal. Appl.
\yr 1996
\vol 30
\issue 2
\pages 137--138
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ziglin, SL, “On the absence of a real-analytic first integral for ABC flow when A=B”, Chaos, 8:1 (1998), 272  crossref  mathscinet  zmath  adsnasa  isi
    2. Ziglin, SL, “On the nonintegrability of the ABC-flow in the case A = B = C”, Doklady Akademii Nauk, 369:2 (1999), 173  mathnet  mathscinet  zmath  isi
    3. Gonzalez-Gascon, F, “Ordered behaviour in force-free magnetic fields”, Physics Letters A, 292:1–2 (2001), 75  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. Haller G., “Distinguished material surfaces and coherent structures in three-dimensional fluid flows”, Physica D, 149:4 (2001), 248–277  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Maciejewski A.J., “Non-integrability in gravitational and cosmological models - Introduction to Ziglin theory and its differential Galois extension”, Restless Universe - Applications of Gravitational N-Body Dynamics To Planetary, Stellar and Galactic Systems, Scottish Universities Summer Schools in Physics Publications, 54, 2001, 361–385  crossref  isi
    6. Ziglin, SL, “Nonintegrability of variational equations in quadratures in some dynamic problems”, Doklady Physics, 47:10 (2002), 750  crossref  mathscinet  adsnasa  isi  scopus  scopus
    7. Maciejewski, A, “Non-integrability of ABC flow”, Physics Letters A, 303:4 (2002), 265  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. S. L. Ziglin, “An Analytic Proof of the Nonintegrability of the ABC-flow for $A=B=C$”, Funct. Anal. Appl., 37:3 (2003), 225–227  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Przybylska, M, “Differential Galois obstructions for integrability of homogeneous Newton equations”, Journal of Mathematical Physics, 49:2 (2008), 022701  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. 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  scopus
    11. Luque A., Peralta-Salas D., “Motion of Charged Particles in Abc Magnetic Fields”, SIAM J. Appl. Dyn. Syst., 12:4 (2013), 1889–1947  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Nishiyama T., “Algebraic Approach To Non-Integrability of Bajer-Moffatt's Steady Stokes Flow”, Fluid Dyn. Res., 46:6 (2014), 061426  crossref  mathscinet  adsnasa  isi  scopus  scopus
    13. 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  scopus
    14. 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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