, Volume 22, Issue 1, pp 121-133

Symmetry Breaking for a System of Two Linear Second-Order Ordinary Differential Equations

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Abstract

A new canonical form for a system of two linear second-orderordinary differential equations (odes) is obtained. The latter isdecisive in unravelling symmetry structure of a system of two linearsecond-order odes. Namely we establish that the point symmetry Liealgebra of a system of two linear second-order odes can be5-, 6-, 7-, 8- or 15-dimensional. This result enhances both the richness andthe complexity of the symmetry structure of linear systems.