SELF-SIMILAR RENORMALIZATION AS EQUATION OF MOTION

We consider a general approximating sequence generated by some kind of perturbation theory or iterative technique. An arbitrary sequence of this sort can be made fastly convergent, or at least semiconvergent, b y means of a renormalization procedure called the method of self-simil ar approximations. We show that such a procedure can be treated as an equation of motion describing the evolution of an autonomous dynamical system. Approximating cascades and flows are introduced. The sequence of approximations composes a trajectory whose form is governed by a s et of governing functions. The sought limit of the sequence plays the role of an attractor. Different types of attractors are analysed. The method is exemplified by an eigenvalue problem.