Abstract
In the present paper we establish the necessary and sufficient conditions for two generalized Abel differential equations to be locally equivalent under the action of the pseudogroup of linear transformations of the form {x ↦ f(x), y ↦ g(x) · y + h(x)}. These conditions are formulated in terms of differential invariants.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Abel, J. Reine. Angew. Math. 4, 309–348 (1829).
P. Appell, J. de Mathématique 5, 361–423 (1889).
E. S. Cheb-Terrab and A. D. Roche, Computer Physics Communications. 01/2000; DOI: 10.1016/S0010-4655(00)00042-4, arXiv:math-ph/0001037v1 (2000).
R. Liouville, Comptes Rendus Acad. Sci. 105, 460–463 (1887).
V. Lychagin, Zb. Pr. Inst. Mat. NAN Ukr. 6 (2), 288–302 (2009).
O. Wone, arXiv:1401.2375[math.DG] (2014).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shurygin, V.V. On the equivalence problem of generalized Abel ODEs under the action of the linear transformations pseudogroup. Lobachevskii J Math 37, 80–86 (2016). https://doi.org/10.1134/S1995080216010091
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080216010091