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The Ermakov equation: A commentary

Leach P.G.L. (University of KwaZulu-Natal, Durban, Republic of South Africa)
Andriopoulos S.K. (University of KwaZulu-Natal, Durban, Republic of South Africa)

We present a short history of the Ermakov equation with an emphasis on its discovery by thewest and the subsequent boost to research into invariants for nonlinear systems although recognizing some of the significant developments in the east. We present the modern context of the Ermakov equation in the algebraic and singularity theory of ordinary differential equations and applications to more divers fields. The reader is referred to the previous article (Appl. Anal. Discrete math., 2 (2008), 123-145) for an english translation of Ermakov's original paper.

Keywords: Ermakov, Pinney, Lewis, sl(2,R), invariant