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Homogeneity and projective equivalence of differential equation fields
1. | Department of Mathematics, Ghent University, Krijgslaan 281, B-9000 Gent, Belgium |
2. | Department of Mathematics, Faculty of Science, The University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic |
References:
[1] |
I. Bucataru, O. A. Constantinescu and M. F. Dahl, A geometric setting for systems of ordinary differential equations,, Int. J. Geom. Methods Mod. Phys., 8 (2011), 1291.
doi: 10.1142/S0219887811005701. |
[2] |
M. Crampin, Homogeneous systems of higher-order ordinary differential equations,, Communications in Mathematics, 18 (2010), 37.
|
[3] |
M. Crampin and D. J. Saunders, The Hilbert-Carathéodory and Poincaré-Cartan forms for higher-order multiple-integral variational problems,, Houston J. Math., 30 (2004), 657.
|
[4] |
F. Faà di Bruno, Sullo sviluppo delle Funzioni,, Annali di Scienze Matematiche e Fisiche, 6 (1855), 479. Google Scholar |
[5] |
I. Kolář, P. W. Michor and J. Slovak, "Natural Operations in Differential Geometry,", Springer-Verlag, (1993).
|
[6] |
B. S. Kruglikov and V. V. Lychagin, Geometry of differential equations,, in, (2008), 725.
|
[7] |
R. Ya. Matsyuk, Higher order variational origin of the Dixon's system and its relation to the quasi-classical 'Zitterbewegung' in general relativity,, preprint, (). Google Scholar |
[8] |
J. Muñoz Masqué and I. M. Pozo Coronado, Parameter-invariant second-order variational problems in one varaiable,, J. Phys. A, 31 (1998), 6225.
doi: 10.1088/0305-4470/31/29/014. |
[9] |
J. J. Stoker, "Differential Geometry,", Pure and Applied Mathematics, (1969).
|
show all references
References:
[1] |
I. Bucataru, O. A. Constantinescu and M. F. Dahl, A geometric setting for systems of ordinary differential equations,, Int. J. Geom. Methods Mod. Phys., 8 (2011), 1291.
doi: 10.1142/S0219887811005701. |
[2] |
M. Crampin, Homogeneous systems of higher-order ordinary differential equations,, Communications in Mathematics, 18 (2010), 37.
|
[3] |
M. Crampin and D. J. Saunders, The Hilbert-Carathéodory and Poincaré-Cartan forms for higher-order multiple-integral variational problems,, Houston J. Math., 30 (2004), 657.
|
[4] |
F. Faà di Bruno, Sullo sviluppo delle Funzioni,, Annali di Scienze Matematiche e Fisiche, 6 (1855), 479. Google Scholar |
[5] |
I. Kolář, P. W. Michor and J. Slovak, "Natural Operations in Differential Geometry,", Springer-Verlag, (1993).
|
[6] |
B. S. Kruglikov and V. V. Lychagin, Geometry of differential equations,, in, (2008), 725.
|
[7] |
R. Ya. Matsyuk, Higher order variational origin of the Dixon's system and its relation to the quasi-classical 'Zitterbewegung' in general relativity,, preprint, (). Google Scholar |
[8] |
J. Muñoz Masqué and I. M. Pozo Coronado, Parameter-invariant second-order variational problems in one varaiable,, J. Phys. A, 31 (1998), 6225.
doi: 10.1088/0305-4470/31/29/014. |
[9] |
J. J. Stoker, "Differential Geometry,", Pure and Applied Mathematics, (1969).
|
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