R. Campoamor-Stursberg
On certain types of point symmetries of of systems of second order ordinary differential equations
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ABSTRACT.  Existence criteria for some generic types of point symmetries of 
systems of $n$-second order ordinary differential equations are 
studied, specially in connection with the generation of semisimple 
subalgebras of symmetries belonging to the simple linear and 
orthogonal types, as well as their maximal dimension and rank. The 
structure of certain time-dependent symmetries, in particular 
scaling symmetries, are also studied, and the structure of the 
subalgebras they span determined. Generic examples illustrating 
the procedure are given.