
Previous Article
Classical field theories of first order and Lagrangian submanifolds of premultisymplectic manifolds
 JGM Home
 This Issue

Next Article
Variational reduction of Lagrangian systems with general constraints
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 
[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 
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 
[1] 
Bernard Dacorogna, Alessandro Ferriero. Regularity and selecting principles for implicit ordinary differential equations. Discrete & Continuous Dynamical Systems  B, 2009, 11 (1) : 87101. doi: 10.3934/dcdsb.2009.11.87 
[2] 
Zvi Artstein. Averaging of ordinary differential equations with slowly varying averages. Discrete & Continuous Dynamical Systems  B, 2010, 14 (2) : 353365. doi: 10.3934/dcdsb.2010.14.353 
[3] 
W. Sarlet, G. E. Prince, M. Crampin. Generalized submersiveness of secondorder ordinary differential equations. Journal of Geometric Mechanics, 2009, 1 (2) : 209221. doi: 10.3934/jgm.2009.1.209 
[4] 
Stefano Maset. Conditioning and relative error propagation in linear autonomous ordinary differential equations. Discrete & Continuous Dynamical Systems  B, 2018, 23 (7) : 28792909. doi: 10.3934/dcdsb.2018165 
[5] 
Aeeman Fatima, F. M. Mahomed, Chaudry Masood Khalique. Conditional symmetries of nonlinear thirdorder ordinary differential equations. Discrete & Continuous Dynamical Systems  S, 2018, 11 (4) : 655666. doi: 10.3934/dcdss.2018040 
[6] 
Hongwei Lou, Weihan Wang. Optimal blowup/quenching time for controlled autonomous ordinary differential equations. Mathematical Control & Related Fields, 2015, 5 (3) : 517527. doi: 10.3934/mcrf.2015.5.517 
[7] 
Jean Mawhin, James R. Ward Jr. Guidinglike functions for periodic or bounded solutions of ordinary differential equations. Discrete & Continuous Dynamical Systems  A, 2002, 8 (1) : 3954. doi: 10.3934/dcds.2002.8.39 
[8] 
Iasson Karafyllis, Lars Grüne. Feedback stabilization methods for the numerical solution of ordinary differential equations. Discrete & Continuous Dynamical Systems  B, 2011, 16 (1) : 283317. doi: 10.3934/dcdsb.2011.16.283 
[9] 
Alessandro Fonda, Fabio Zanolin. Bounded solutions of nonlinear second order ordinary differential equations. Discrete & Continuous Dynamical Systems  A, 1998, 4 (1) : 9198. doi: 10.3934/dcds.1998.4.91 
[10] 
Bin Wang, Arieh Iserles. Dirichlet series for dynamical systems of firstorder ordinary differential equations. Discrete & Continuous Dynamical Systems  B, 2014, 19 (1) : 281298. doi: 10.3934/dcdsb.2014.19.281 
[11] 
Ping Lin, Weihan Wang. Optimal control problems for some ordinary differential equations with behavior of blowup or quenching. Mathematical Control & Related Fields, 2018, 8 (3&4) : 809828. doi: 10.3934/mcrf.2018036 
[12] 
Lijun Yi, Zhongqing Wang. Legendre spectral collocation method for secondorder nonlinear ordinary/partial differential equations. Discrete & Continuous Dynamical Systems  B, 2014, 19 (1) : 299322. doi: 10.3934/dcdsb.2014.19.299 
[13] 
BenYu Guo, ZhongQing Wang. A spectral collocation method for solving initial value problems of first order ordinary differential equations. Discrete & Continuous Dynamical Systems  B, 2010, 14 (3) : 10291054. doi: 10.3934/dcdsb.2010.14.1029 
[14] 
Wen Li, Song Wang, Volker Rehbock. A 2ndorder onepoint numerical integration scheme for fractional ordinary differential equations. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 273287. doi: 10.3934/naco.2017018 
[15] 
Yuriy Golovaty, Anna MarciniakCzochra, Mariya Ptashnyk. Stability of nonconstant stationary solutions in a reactiondiffusion equation coupled to the system of ordinary differential equations. Communications on Pure & Applied Analysis, 2012, 11 (1) : 229241. doi: 10.3934/cpaa.2012.11.229 
[16] 
Angelo Favini, Yakov Yakubov. Regular boundary value problems for ordinary differentialoperator equations of higher order in UMD Banach spaces. Discrete & Continuous Dynamical Systems  S, 2011, 4 (3) : 595614. doi: 10.3934/dcdss.2011.4.595 
[17] 
Yanfei Lu, Qingfei Yin, Hongyi Li, Hongli Sun, Yunlei Yang, Muzhou Hou. Solving higher order nonlinear ordinary differential equations with least squares support vector machines. Journal of Industrial & Management Optimization, 2017, 13 (5) : 122. doi: 10.3934/jimo.2019012 
[18] 
Janosch Rieger. The Euler scheme for state constrained ordinary differential inclusions. Discrete & Continuous Dynamical Systems  B, 2016, 21 (8) : 27292744. doi: 10.3934/dcdsb.2016070 
[19] 
J. Gwinner. On differential variational inequalities and projected dynamical systems  equivalence and a stability result. Conference Publications, 2007, 2007 (Special) : 467476. doi: 10.3934/proc.2007.2007.467 
[20] 
Tomasz Kapela, Piotr Zgliczyński. A Lohnertype algorithm for control systems and ordinary differential inclusions. Discrete & Continuous Dynamical Systems  B, 2009, 11 (2) : 365385. doi: 10.3934/dcdsb.2009.11.365 
2018 Impact Factor: 0.525
Tools
Metrics
Other articles
by authors
[Back to Top]