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Homogeneity and projective equivalence of differential equation fields
1.  Department of Mathematics, Ghent University, Krijgslaan 281, B9000 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. Google Scholar 
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M. Crampin, Homogeneous systems of higherorder ordinary differential equations,, Communications in Mathematics, 18 (2010), 37. Google Scholar 
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M. Crampin and D. J. Saunders, The HilbertCarathéodory and PoincaréCartan forms for higherorder multipleintegral variational problems,, Houston J. Math., 30 (2004), 657. Google Scholar 
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F. Faà di Bruno, Sullo sviluppo delle Funzioni,, Annali di Scienze Matematiche e Fisiche, 6 (1855), 479. Google Scholar 
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I. Kolář, P. W. Michor and J. Slovak, "Natural Operations in Differential Geometry,", SpringerVerlag, (1993). Google Scholar 
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B. S. Kruglikov and V. V. Lychagin, Geometry of differential equations,, in, (2008), 725. Google Scholar 
[7] 
R. Ya. Matsyuk, Higher order variational origin of the Dixon's system and its relation to the quasiclassical 'Zitterbewegung' in general relativity,, preprint, (). Google Scholar 
[8] 
J. Muñoz Masqué and I. M. Pozo Coronado, Parameterinvariant secondorder variational problems in one varaiable,, J. Phys. A, 31 (1998), 6225. doi: 10.1088/03054470/31/29/014. Google Scholar 
[9] 
J. J. Stoker, "Differential Geometry,", Pure and Applied Mathematics, (1969). Google Scholar 
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. Google Scholar 
[2] 
M. Crampin, Homogeneous systems of higherorder ordinary differential equations,, Communications in Mathematics, 18 (2010), 37. Google Scholar 
[3] 
M. Crampin and D. J. Saunders, The HilbertCarathéodory and PoincaréCartan forms for higherorder multipleintegral variational problems,, Houston J. Math., 30 (2004), 657. Google Scholar 
[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,", SpringerVerlag, (1993). Google Scholar 
[6] 
B. S. Kruglikov and V. V. Lychagin, Geometry of differential equations,, in, (2008), 725. Google Scholar 
[7] 
R. Ya. Matsyuk, Higher order variational origin of the Dixon's system and its relation to the quasiclassical 'Zitterbewegung' in general relativity,, preprint, (). Google Scholar 
[8] 
J. Muñoz Masqué and I. M. Pozo Coronado, Parameterinvariant secondorder variational problems in one varaiable,, J. Phys. A, 31 (1998), 6225. doi: 10.1088/03054470/31/29/014. Google Scholar 
[9] 
J. J. Stoker, "Differential Geometry,", Pure and Applied Mathematics, (1969). Google Scholar 
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