Abstract
In this work a new approach for classification of ordinary differential equations is suggested. The field of differential invariants is described, basic differential invariants are found, and contact classification of ordinary differential equations in terms of these invariants is obtained.
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D. Alekseevskii, A. Vinogradov, and V. Lychagin, “Basic ideas and concepts of differential geometry,” Geometry I. Encycl.Math. Sci. VINITI. 28, 255 (1991).
B. Dubrov, RussianMathematics (Iz VUZ) 50 (1), 73 (2006).
W. Chen and H. Li, Acta Scientiarum Naturalium Universitat is Pekinensis 35 (3), 285–296 (1999).
S. Chern, Sci. Rep. Nat. Tsing Hua Univ. 4, 97–111 (1950).
B. Dubrov, Differential Geometry and Its Applications (Proc. Conf., Opava, August 27–31, 2001), pp. 73–84.
B. Doubrov, B. Komrakov, and T. Morimoto, Lobachevskii J. of Mathematics 3, 39–71 (1999).
B. Kruglikov, “Point classification of 2nd order ODEs: Tresse classification revisited and beyond,” arXiv: 0809.4653.
B. Kriglikov and V. Lychagin, “Global Lie–Tresse theorem,” arXiv: 1111.5480v1.
V. V. Lychagin, Acta ApplicandaeMathematicae 109 (1), 211 (2010).
S. Sternberg, Lectures on Differential Geometry (Prentice Hall, Inc. Englewood Cliffs, N.J., 1964).
A. Tresse, “Détermination des invariants ponctuels de l’ équation différentielle ordinaire du second ordre y” = ω(x, y, y’),” Ph. D. Dissertation (Universtat Leipzig, Leipzig, 1896).
V. Yumaguzhin, “Differential invariants of 2-order ODEs, I,” arXiv: 0804.0674v1.
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Bibikov, P. Differential invariants and contact classification of ordinary differential equations. Lobachevskii J Math 36, 245–249 (2015). https://doi.org/10.1134/S199508021503004X
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DOI: https://doi.org/10.1134/S199508021503004X