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arXiv · 1304.7446

Integrable maps from Galois differential algebras, Borel transforms and number sequences

Piergiulio Tempesta
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Abstract

A new class of integrable maps, obtained as lattice versions of polynomial dynamical systems is introduced. These systems are obtained by means of a discretization procedure that preserves several analytic and algebraic properties of a given differential equation, in particular symmetries and integrability [40]. Our approach is based on the properties of a suitable Galois differential algebra, that we shall call a Rota algebra. A formulation of the procedure in terms of category theory is proposed. In order to render the lattice dynamics confined, a Borel regularization is also adopted. As a byproduct of the theory, a connection between number sequences and integrability is discussed.

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Piergiulio Tempesta. 2013-06-16. Integrable maps from Galois differential algebras, Borel transforms and number sequences. https://doi.org/10.1016/j.jde.2013.04.008

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