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On certain types of point symmetries of of systems of second order ordinary differential equations
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.