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This work presents a classical Lie point symmetry analysis of atwo-component, non-isospectral Lax pair of a hierarchy of partial differentialequations in $2+1$ dimensions, which can be considered as a modified version ofthe Camassa-Holm hierarchy in $2+1$ dimensions. A classification of reductionsfor this spectral problem is performed. Non-isospectral reductions in $1+1$dimensions are considered of remarkable interest.

Integrable $1+1$ dimensional hierarchies arising from the reduction of a nonisospectral problem in $2+1$ dimensions