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Linearisable mappings and their explicit integration

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Discrete Integrable Systems

After a short introduction concerning the presence of linearisable systems in the Painlev and Gambier classications we shall present recent results on linearisable mappings. The study of discrete linearisable second-order mappings revealed the existence of three main families of such systems. The first ones are the projective mappings, the second group are the linearisable mappings of Gambier type and their various degenerate forms and third family is known under the name of linearisable mapping of third kind. We shall present the linearisable mappings belonging to these families, derive their nonautonomous forms and give their explicit integration.

This talk is part of the Isaac Newton Institute Seminar Series series.

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