TL;DR
This paper classifies the possible symmetry algebra dimensions of general analytic second order ODEs, showing they range from 0 to 8 except 7, with the maximum dimension indicating local trivializability.
Contribution
It provides a complete classification of the symmetry algebra dimensions for second order ODEs, including cases beyond principal type.
Findings
Symmetry algebra dimensions range from 0 to 8, excluding 7.
Maximum symmetry dimension (8) implies the ODE is locally trivializable.
All dimensions between 0 and 8 are realizable except for 7.
Abstract
It is demonstrated that point symmetry algebras of general analytic second order ODEs, not necessary of principal type, can have all dimensions between 0 and 8 except for 7. For the symmetry dimension 8 the ODE must be locally trivializable.
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