  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.
