1304.7446 (Piergiulio Tempesta)

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

Piergiulio Tempesta

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 make 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.

View original: http://arxiv.org/abs/1304.7446