Antiquantization as a specific way from the Statistical physics to the Regular physics

Abstract

An extended analysis is given of links between linear Heun class equations and the nonlinear Painlevé equations. For linear equations, Heun class equations, deformed Heun class equations, parallel to various first-order systems, are chosen. The role of an accessory parameter in each case is explained. Links to isomonodromic property is traced. The complete list of Painlevé equations in an nonconventional manner is presented.