Abstract: This paper introduces some related concepts of pansystems analysis (such as pansystem, pansystem space, pansystem logic space, pometric pansystem, etc), and develops the convex set theory, Banach's theorem of completeness, Lax equivalence theory, theorems of Kuhn-Tucker type and Dubovitsky-Milutin type into the pometric (partial ordered metric) pansystem forms, they are different from traditional results. Furthermore, the general stability of operator equations and MSP transforming principles of approximation are investigated.

Key words: nonlinear dynamical system, modified normal form approach, symbolic calculations