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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Tempesta, Piergiulio

关键词: Differential equations;    Integrable maps;    Galois differential algebras;    Category theory;    Recurrences;    Number sequences;   

DOI  :  10.1016/j.jde.2013.04.008

来源: Elsevier

【 摘 要 】

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 (see Tempesta, 2010 [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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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