DIS

Abstract

New discretization of Complex Analysis was developed few years ago in the joint works of the present author and I.Dynnikov. Some Fundamental Ideas were borrowed from the Theory of Completely Integrable Systems. This problem is treated as a Discretization of Cauchy-Riemann Linear Operator. Geometric Discretization of Conformal Maps has nothing to do with our work. It is based on the Equilateral Triangle Lattice. Classical Discretization was based on the Quadrilateral (Square) Lattice. Many Scientists developed it. However, it turnes out that Equilateral Triangle Lattice preserves much better some features of Complex Analysis unifying it with Modern Theory of Systems Integrable by The Inverse Scattering Transform.