Geodesic
The moving frames for differential equations. I. The change of independent variable
Archivum mathematicum, Tome 39 (2003) no. 4, pp. 317-333 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The article concerns the symmetries of differential equations with short digressions to the underdetermined case and the relevant differential equations with delay. It may be regarded as an introduction into the method of moving frames relieved of the geometrical aspects: the stress is made on the technique of calculations employing only the most fundamental properties of differential forms. The present Part I is devoted to a single ordinary differential equation subjected to the change of the independent variable, the unknown function is preserved.
The article concerns the symmetries of differential equations with short digressions to the underdetermined case and the relevant differential equations with delay. It may be regarded as an introduction into the method of moving frames relieved of the geometrical aspects: the stress is made on the technique of calculations employing only the most fundamental properties of differential forms. The present Part I is devoted to a single ordinary differential equation subjected to the change of the independent variable, the unknown function is preserved.
Classification : 34A25, 34A26, 34C14, 53B21
Keywords: moving coframe; equivalence of differential equations; symmetry of differential equations; differential invariant; Maurer-Cartan form 
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Tryhuk, Václav; Dlouhý, Oldřich. The moving frames for differential equations. I. The change of independent variable. Archivum mathematicum, Tome 39 (2003) no. 4, pp. 317-333. http://geodesic.mathdoc.fr/item/ARM_2003_39_4_a7/

[1] Aczél J.: Über Zusammenhänge zwischen Differential– und Funktionalgleichungen. Jahresber. Deutsch. Math. Ver. 71 (1969), 55–57. | MR | Zbl

[2] Awane A., Goze M.: Pfaffian Systems, k-symplectic Systems. Kluwer Academic Publischers (Dordrecht–Boston–London), 2000. | MR | Zbl

[3] Borůvka O.: Linear Differential Transformations of the Second Order. The English Univ. Press, London, 1971. | MR

[4] Bryant R., Chern S. S., Goldschmidt H., Griffiths P. A.: Exterior differential systems. Mat. Sci. Res. Inst. Publ. 18, Springer-Verlag 1991. | MR | Zbl

[5] Cartan E.: Les systémes différentiels extérieurs et leurs applications géometriques. Act. Scient. et Ind. 994 (1945). | MR | Zbl

[6] Cartan E.: Sur la structure des groupes infinis de transformations. Ann. Ec. Norm. 3-e serie, t. XXI, 1904 (also Oeuvres Complètes, Partie II, Vol 2, Gauthier–Villars, Paris 1953).

[7] Chrastina J.: Transformations of differential equations. Equadiff 9 CD ROM, Papers, Masaryk univerzity, Brno 1997, 83–92.

[8] Chrastina J.: The formal theory of differential equations. Folia Fac. Scient. Nat. Univ. Masarykianae Brunensis, Mathematica 6, 1998. | MR | Zbl

[9] Gardner R. B.: The method of equivalence and its applications. CBMS–NSF Regional Conf. in Appl. Math. 58, 1989. | MR | Zbl

[10] Moór A., Pintér L.: Untersuchungen über den Zusammenhang von Differential– und Funktionalgleichungen. Publ. Math. Debrecen 13 (1966), 207–223. | MR | Zbl

[11] Neuman F.: Global Properties of Linear Ordinary Differential Equations. Mathematics and Its Applications (East European Series) 52, Kluwer Acad. Publ., Dordrecht–Boston–London, 1991. | MR | Zbl

[12] Posluszny J., Rubel L. A.: The motion of an ordinary differential equation. J. Differential Equations 34 (1979), 291–302. | MR

[13] Sharpe R. V.: Differential geometry. Graduate Texts in Math. 166, Springer Verlag, 1997. | MR | Zbl

[14] Tryhuk V.: On transformations $z(t)=y(\varphi (t))$ of ordinary differential equations. Czech. Math. J., 50(125) (2000), Praha, 509–518. | MR | Zbl