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 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

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

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
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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• http://mi.mathnet.ru/eng/faa3447
• https://doi.org/10.4213/faa3447
• http://mi.mathnet.ru/eng/faa/v51/i4/p16

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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
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
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
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
5. Bibikov P.V., “Classification of Second Order Linear Ordinary Differential Equations With Rational Coefficients”, Lobachevskii J. Math., 40:1, SI (2019), 14–23
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