### ¡Nos trasladamos! E-Prints cerrará el 7 de junio.

En las próximas semanas vamos a migrar nuestro repositorio a una nueva plataforma con muchas funcionalidades nuevas. En esta migración las fechas clave del proceso son las siguientes:

• 7 de junio: congelación de E-Prints. A partir de este momento, no se podrá hacer ningún depósito ni cambio, modificación o edición.
• 12 al 30 de junio: migración de E-Prints a Docta Complutense, comprobación y visto bueno de la migración
• 3 de julio: entrada en producción de Docta Complutense

Es muy importante que cualquier depósito se realice en E-Prints Complutense antes del 7 de junio. En caso de urgencia para realizar un depósito, se puede comunicar a docta@ucm.es.

# Symmetries of differential equations. IV

### Impacto View download statistics for this eprint

Altmetric Buscar en Google Scholar™

González Gascón, F. and González López, Artemio (1983) Symmetries of differential equations. IV. Journal of mathematical physics, 24 (8). pp. 2006-2021. ISSN 0022-2488  Preview 1MB

Official URL: http://dx.doi.org/10.1063/1.525960 ==>>> Export to other formats

## Abstract

By an application of the geometrical techniques of Lie, Cohen, and Dickson it is shown that a system of differential equations of the form [x^(r_i)]_i = F_i(where r_i > 1 for every i = 1 , ... ,n) cannot admit an infinite number of pointlike symmetry vectors. When r_i = r for every i = 1, ... ,n, upper bounds have been computed for the maximum number of independent symmetry vectors that these systems can possess: The upper bounds are given by 2n_ 2 + nr + 2 (when r> 2), and by 2n_2 + 4n + 2 (when r = 2). The group of symmetries of ͞x^r = ͞0 (r> 1) has also been computed, and the result obtained shows that when n > 1 and r> 2 the number of independent symmetries of these equations does not attain the upper bound 2n _2 + nr + 2, which is a common bound for all systems of differential equations of the form ͞x^r = F[t, ͞x, ... , ͞x^(r - 1 )] when r> 2. On the other hand, when r = 2 the first upper bound obtained has been reduced to the value n^2 + 4n + 3; this number is equal to the number of independent symmetry vectors of the system ͞x= ͞0, and is also a common bound for all systems of the form ͞x = ͞F (t ,͞x, ‾̇x).

Item Type: Article ©1983 American Institute of Physics.It is a pleasure to express our gratitude to Dr. C. Ruiz and Dr. M. Amores for useful discussions with them and for providing some bibliography. It is also a pleasure to acknowledge the constant encouragement given by M. C. Hidalgo-Brinquis. Physics, Mathematical Sciences > Physics > Physics-Mathematical modelsSciences > Physics > Mathematical physics 32931 28 Aug 2015 08:37 10 Dec 2018 15:10