ON THE PROBLEM OF CLASSIFICATION OF POLYNOMIAL ENDOMORPHISMS OF THE PLANE

Abstract

The paper is a continuation of the author's paper [5] (Math. USSR Sbornik 6 (1968), 97-114).§1 concerns the iterations of a polynomial of degree on a singular set . It is assumed that the critical points of lie either in the domains of attraction of finite attracting cycles or at infinity. The theorems of [5] (Theorem 1 concerning the topological isomorphism of the transformation and of a shift on the space of one-sided -ary sequences with a finite number of identifications; Theorem 2: ) are generalized for the case of a disconnected .In §2 the author investigates the iterations of on the entire plane . He shows (Theorem 3) that the dynamical systems and are topologically isomorphic for sufficiently small in the case of polynomials satisfying one of the hypotheses of §1 and a certain coarse condition of nonconjugacy of the iterations of distinct critical points.Hypothesis: the set of structurally stable mappings investigated in the paper is everywhere dense in the space of coefficients.Nine figures; bibliography of eight titles.