González Gascón, F.González López, Artemio2023-06-212023-06-2119830022-248810.1063/1.525960https://hdl.handle.net/20.500.14352/64991©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.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).engjournal articlehttp://dx.doi.org/10.1063/1.525960http://scitation.aip.orgopen access51-73PhysicsMathematicalFísica-Modelos matemáticosFísica matemática