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Funktsional. Anal. i Prilozhen., 2017, Volume 51, Issue 4, Pages 16–25 (Mi faa3447)  

This article is cited in 5 scientific papers (total in 5 papers)

On Lie’s problem and differential invariants of ODEs $y-F(x,y)$

P. V. Bibikov

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

Abstract: A point classification of ordinary differential equations of the form $y-F(x,y)$ is considered. The algebra of differential invariants of the action of the point symmetry pseudogroup on the right-hand sides of equations of the form $y-F(x,y)$ is calculated, and Lie's problem on the point equivalence of such equations is solved.

Keywords: point transformation, pseudogroup, jet space, differential invariant, Lie's problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-60018
This work is supported by RFBN grant mol_a_dk 16-31-60018.


DOI: https://doi.org/10.4213/faa3447

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English version:
Functional Analysis and Its Applications, 2017, 51:4, 255–262

Bibliographic databases:

UDC: 517.911+514.763.52+514.763.8
Received: 04.07.2016
Revised: 09.12.2016
Accepted:24.01.2017

Citation: P. V. Bibikov, “On Lie’s problem and differential invariants of ODEs $y-F(x,y)$”, Funktsional. Anal. i Prilozhen., 51:4 (2017), 16–25; Funct. Anal. Appl., 51:4 (2017), 255–262

Citation in format AMSBIB
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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. P. V. Bibikov, “Generalized Lie problem and differential invariants for the third order ODEs”, Lobachevskii J. Math., 38:4 (2017), 622–629  crossref  mathscinet  zmath  isi  scopus
    2. P. Bibikov, A. Malakhov, “On classification problems in the theory of differential equations: Algebra + geometry”, Publ. Inst. Math. Beograd, 103:117 (2018), 33–52  crossref  isi  scopus
    3. P. V. Bibikov, “On Differential Invariants and Classification of Ordinary Differential Equations of the Form $y-A(x,y)y'+B(x,y)$”, Math. Notes, 104:2 (2018), 167–175  mathnet  crossref  crossref  isi  elib
    4. P. Bibikov, “On the Lie problem in PDEs and effective classification of the differential equations with algebraic coefficients”, J. Geom. Phys., 136 (2019), 39–44  crossref  mathscinet  zmath  isi  scopus
    5. Bibikov P.V., “Classification of Second Order Linear Ordinary Differential Equations With Rational Coefficients”, Lobachevskii J. Math., 40:1, SI (2019), 14–23  crossref  mathscinet  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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