Complete Symmetry Groups of Ordinary Differential Equations and Their Integrals: Some Basic Considerations

Abraham-Shrauner, 1993, Hidden symmetries of nonlinear ordinary differential equations, 29, 1

Abraham-Shrauner, 1995, Hidden and contact symmetries of ordinary differential equations, J. Phys. A., 28, 6707, 10.1088/0305-4470/28/23/020

S. É. Bouquet, and, P. G. L. Leach, Symmetry, Singularities and Integrability in Complex Dynamics VII: Integrating Factors and Symmetries, preprint, GEODYSYC, University of the Aegean, Karlovassi, Greece, 2000.

Ermakov, 1880, Second order differential equations: Conditions of complete integrability, Univ. Izvestia Kiev Ser. III, 9, 1

Flessas, 1994, Remarks on the symmetry Lie algebras of first integrals of scalar third order ordinary differential equations with maximal symmetry, Bull. Greek Math. Soc., 36, 63

Flessas, 1997, Characterisation of the algebraic properties of first integrals of scalar ordinary differential equations of maximal symmetry, J. Math. Anal. Appl., 212, 349, 10.1006/jmaa.1997.5506

Govinder, 1995, The algebraic structure of the first integrals of third-order linear equations, J. Math. Anal. Appl., 193, 114, 10.1006/jmaa.1995.1225

Kamke, 1983

Krause, 1994, On the complete symmetry group of the classical Kepler system, J. Math. Phys., 35, 5734, 10.1063/1.530708

Leach, 1991, Generalised Ermakov systems, Phys. Lett. A, 158, 102, 10.1016/0375-9601(91)90908-Q

Leach, 1988, Maximal subalgebra associated with a first integral of a system possessing sl(3,R) algebra, J. Math. Phys., 29, 1807, 10.1063/1.527882

P. G. L. Leach, M. C. Nucci, and, S. Cotsakis, Symmetry, Singularities and Integrability in Complex Dynamics V: Complete Symmetry Groups, preprint, GEODYSYC, University of the Aegean, Karlovassi, Greece, 2000.

Lie, 1967

Mahomed, 1985, The linear symmetries of a nonlinear differential equation, Quæst Math., 8, 241

Mahomed, 1990, Symmetry Lie algebras of nth order ordinary differential equations, J. Math. Anal. Appl., 151, 80, 10.1016/0022-247X(90)90244-A

Mubarakzyanov, 1963, On solvable Lie algebras, Izv. Vyssh. Uchebn Zaved. Mat., 32, 114

Mubarakzyanov, 1963, Classification of real structures of five-dimensional Lie algebras, Izv. Vyssh. Uchebn. Zaved. Mat., 34, 99

Mubarakzyanov, 1963, Classification of solvable six-dimensional Lie algebras with one nilpotent base element, Izv. Vyssh. Uchebn. Zaved. Mat., 35, 104

Nucci, 1996, Interactive REDUCE programs for calculating Lie point, non-classical, Lie-Bäcklund, and approximate symmetries of differential equations: Manual and floppy disk, III, 415

Nucci, 1996, The complete symmetry group can be derived by Lie group analysis, J. Math. Phys., 37, 1772, 10.1063/1.531496

Nucci, 2001, The harmony in the Kepler and related problems, J. Math. Phys., 42, 746, 10.1063/1.1337614

Pinney, 1950, The nonlinear differential equation y′′(x)+p(x)y+cy−3=0, Proc. Amer. Math. Soc., 1, 681

A. C. Richard, Painlevé Analysis and Partial Integrability of Some Dynamical Systems, dissertation, University of Natal, Durban, Republic of South Africa, 1995.