Gerardo Torres del Castillo¹ - Magdalena Marciano Melchor²

¹Departamento de Física Matemática. Instituto de Ciencias. Universidad Autónoma de Puebla. Apartado postal 1152. 72001 Puebla, México.

e-mail: gtorres@fcfm.buap.mx

²Facultad de Ciencias Físico Matemáticas. Universidad Autónoma de Puebla. Apartado postal 1152. 72001 Puebla, México

e-mail: est068@fcfm.buap.mx

Abstract. A proof of the Lie theorem which relates the symmetries of a first order differential equation (or of a linear differential form) with its integrating factors is given. It is shown that a similar result partially applies for systems of linear differential forms and ordinary differential equations of any order.

2000 Mathematics Subject Classification. Primary: 34A26, 54H15. Secondary: 58D19, 35F05.

Resumen. Se da una prueba del teorema de Lie que relaciona las simetrías de una ecuación diferencial de primer orden(o de una forma diferencial lineal) con su factor integrante. Se demuestra que un resultado similar parcialmente aplica para sistemas de formas diferenciales lineales y ecuaciones diferenciales ordinarias de cualquier orden.

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[1] G. F. Simmons, Differential Equations. With Applications and Historical Notes, 2nd ed., 9. McGraw-Hill, New York, 1991.        [ Links ]

[2] N. H. Ibragimov, Sophus Lie and Harmony in Mathematical Physics, on the 150th Anniversary of His Birth, The Mathematical Intelligencer 16, 20 (1994).        [ Links ]

[3] H. Stephani, Differential Equations: Their Solution Using Symmetries, Cambridge University Press, Cambridge, 1989.        [ Links ]

[4] L. Dresner, Applications of Lie's Theory of Ordinary and Partial Differential Equations, Institute of Physics, Bristol, 1999.        [ Links ]

[5] P. E. Hydon, Symmetry Methods for Differential Equations: A Beginner's Guide, Cambridge University Press, Cambridge, 2000.        [ Links ]

[6] C. von Westenholz, Differential Forms in Mathematical Physics, North-Holland, Amsterdam, 1981.        [ Links ]

(Recibido en agosto de 2005. Aceptado en noviembre de 2005)