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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), 12911327. doi: 10.1142/S0219887811005701. 
[2] 
M. Crampin, Homogeneous systems of higherorder ordinary differential equations, Communications in Mathematics, 18 (2010), 3750. 
[3] 
M. Crampin and D. J. Saunders, The HilbertCarathéodory and PoincaréCartan forms for higherorder multipleintegral variational problems, Houston J. Math., 30 (2004), 657689. 
[4] 
F. Faà di Bruno, Sullo sviluppo delle Funzioni, Annali di Scienze Matematiche e Fisiche, 6 (1855), 479480. 
[5] 
I. Kolář, P. W. Michor and J. Slovak, "Natural Operations in Differential Geometry," SpringerVerlag, Berlin, 1993. 
[6] 
B. S. Kruglikov and V. V. Lychagin, Geometry of differential equations, in "Handbook of Global Analysis" (eds. D. Krupka and D. J. Saunders), 1214, Elsevier Sci. B. V., Amsterdam, (2008), 725771. 
[7] 
R. Ya. Matsyuk, Higher order variational origin of the Dixon's system and its relation to the quasiclassical 'Zitterbewegung' in general relativity,, preprint, (). 
[8] 
J. Muñoz Masqué and I. M. Pozo Coronado, Parameterinvariant secondorder variational problems in one varaiable, J. Phys. A, 31 (1998), 62256242. doi: 10.1088/03054470/31/29/014. 
[9] 
J. J. Stoker, "Differential Geometry," Pure and Applied Mathematics, Vol. XX, Interscience Publishers John Wiley & Sons, New YorkLondonSydney, 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), 12911327. doi: 10.1142/S0219887811005701. 
[2] 
M. Crampin, Homogeneous systems of higherorder ordinary differential equations, Communications in Mathematics, 18 (2010), 3750. 
[3] 
M. Crampin and D. J. Saunders, The HilbertCarathéodory and PoincaréCartan forms for higherorder multipleintegral variational problems, Houston J. Math., 30 (2004), 657689. 
[4] 
F. Faà di Bruno, Sullo sviluppo delle Funzioni, Annali di Scienze Matematiche e Fisiche, 6 (1855), 479480. 
[5] 
I. Kolář, P. W. Michor and J. Slovak, "Natural Operations in Differential Geometry," SpringerVerlag, Berlin, 1993. 
[6] 
B. S. Kruglikov and V. V. Lychagin, Geometry of differential equations, in "Handbook of Global Analysis" (eds. D. Krupka and D. J. Saunders), 1214, Elsevier Sci. B. V., Amsterdam, (2008), 725771. 
[7] 
R. Ya. Matsyuk, Higher order variational origin of the Dixon's system and its relation to the quasiclassical 'Zitterbewegung' in general relativity,, preprint, (). 
[8] 
J. Muñoz Masqué and I. M. Pozo Coronado, Parameterinvariant secondorder variational problems in one varaiable, J. Phys. A, 31 (1998), 62256242. doi: 10.1088/03054470/31/29/014. 
[9] 
J. J. Stoker, "Differential Geometry," Pure and Applied Mathematics, Vol. XX, Interscience Publishers John Wiley & Sons, New YorkLondonSydney, 1969. 
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