The moving frames for differential equations. I. The change of independent variable

Václav Tryhuk; Oldřich Dlouhý

Archivum Mathematicum (2003)

  • Volume: 039, Issue: 4, page 317-333
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Tryhuk, Václav, and Dlouhý, Oldřich. "The moving frames for differential equations. I. The change of independent variable." Archivum Mathematicum 039.4 (2003): 317-333. <http://eudml.org/doc/249139>.

@article{Tryhuk2003,
abstract = {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.},
author = {Tryhuk, Václav, Dlouhý, Oldřich},
journal = {Archivum Mathematicum},
keywords = {moving coframe; equivalence of differential equations; symmetry of differential equations; differential invariant; Maurer-Cartan form; moving coframe; equivalence of differential equations; symmetry of differential equations; differential invariant; Maurer-Cartan form},
language = {eng},
number = {4},
pages = {317-333},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The moving frames for differential equations. I. The change of independent variable},
url = {http://eudml.org/doc/249139},
volume = {039},
year = {2003},
}

TY - JOUR
AU - Tryhuk, Václav
AU - Dlouhý, Oldřich
TI - The moving frames for differential equations. I. The change of independent variable
JO - Archivum Mathematicum
PY - 2003
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 039
IS - 4
SP - 317
EP - 333
AB - 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.
LA - eng
KW - moving coframe; equivalence of differential equations; symmetry of differential equations; differential invariant; Maurer-Cartan form; moving coframe; equivalence of differential equations; symmetry of differential equations; differential invariant; Maurer-Cartan form
UR - http://eudml.org/doc/249139
ER -

References

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  9. Gardner R. B., The method of equivalence and its applications, CBMS–NSF Regional Conf. in Appl. Math. 58, 1989. (1989) Zbl0694.53027MR1062197
  10. Moór A., Pintér L., Untersuchungen über den Zusammenhang von Differential– und Funktionalgleichungen, Publ. Math. Debrecen 13 (1966), 207–223. (1966) Zbl0199.15301MR0206445
  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. (1991) Zbl0784.34009MR1192133
  12. Posluszny J., Rubel L. A., The motion of an ordinary differential equation, J. Differential Equations 34 (1979), 291–302. (1979) MR0550047
  13. Sharpe R. V., Differential geometry, Graduate Texts in Math. 166, Springer Verlag, 1997. (1997) Zbl0876.53001MR1453120
  14. Tryhuk V., On transformations z ( t ) = y ( ϕ ( t ) ) of ordinary differential equations, Czech. Math. J., 50(125) (2000), Praha, 509–518. Zbl1079.34505MR1777472

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