RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Ufimsk. Mat. Zh., 2012, Volume 4, Issue 4, Pages 38–44 (Mi ufa166)  

On automorphic systems of differential equations and $\mathrm{GL}_2(\mathbb C)$-orbits of binary forms

P. V. Bibikov

Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: In the work we introduce a new method for studying the classical algebraic problem of classifying $\mathrm{GL}_2(\mathbb C)$-orbits of binary forms with the help of differential equations. We construct and study an automorphic system of differential equations $\mathcal S$ of the fourth order, whose solution space coincides with the $\mathrm{GL}_2(\mathbb C)$-orbit of a fixed binary form $f$. The system $\mathcal S$ is integrable in cases when it is of the second and third order. In the most difficult case, when the system is of the fourth order, we prove that the system $\mathcal S$ can be reduced to a first order differential equation of the Abel type and a linear partial differential equation of the first order.

Keywords: binary forms, jet space, differential invariants, automorphic differential equations.

Full text: PDF file (446 kB)
References: PDF file   HTML file
UDC: 517.957+512.745
Received: 30.09.2011

Citation: P. V. Bibikov, “On automorphic systems of differential equations and $\mathrm{GL}_2(\mathbb C)$-orbits of binary forms”, Ufimsk. Mat. Zh., 4:4 (2012), 38–44

Citation in format AMSBIB
\Bibitem{Bib12}
\by P.~V.~Bibikov
\paper On automorphic systems of differential equations and $\mathrm{GL}_2(\mathbb C)$-orbits of binary forms
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 4
\pages 38--44
\mathnet{http://mi.mathnet.ru/ufa166}


Linking options:
  • http://mi.mathnet.ru/eng/ufa166
  • http://mi.mathnet.ru/eng/ufa/v4/i4/p38

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Уфимский математический журнал
    Number of views:
    This page:152
    Full text:60
    References:27
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019