Geodesic
On the problem of classification of polynomial endomorphisms of the plane
Sbornik. Mathematics, Tome 9 (1969) no. 3, pp. 345-364 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is a continuation of the author's paper [1] (Math. Sb. (N.S.) 77(119) (1968), 105–124). § 1 concerns the iterations of a polynomial $P(z)$ of degree $d>1$ on a singular set $\mathscr F$. It is assumed that the critical points of $P^{-1}(z)$ lie either in the domains of attraction of finite attracting cycles or at infinity. The theorems of [1] (Theorem 1 concerning the topological isomorphism of the transformation $P(z)/\mathscr F$ and of a shift on the space of one-sided $d$-ary sequences with a finite number of identifications; Theorem 2: $P/\mathscr F\approx P_\varepsilon/\mathscr F_\varepsilon$) are generalized for the case of a disconnected $\mathscr F$. In § 2 the author investigates the iterations of $P(z)$ on the entire plane $\pi$. He shows (Theorem 3) that the dynamical systems $P/\pi$ and $P_\varepsilon/\pi$ are topologically isomorphic for sufficiently small $|\varepsilon|$ 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 $z\to P(z)$ investigated in the paper is everywhere dense in the space of coefficients. Figures : 9. Bibliography: 8 titles. 
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M. V. Jakobson. On the problem of classification of polynomial endomorphisms of the plane. Sbornik. Mathematics, Tome 9 (1969) no. 3, pp. 345-364. http://geodesic.mathdoc.fr/item/SM_1969_9_3_a4/

[1] P. Fatou, “Sur les équations fonctionnelles, I”, Bull. Soc. Math. France, 47 (1919), 161–271 | MR

[2] P. Fatou, “Sur les equations fonctionnelles, II, III”, Bull. Soc. Math. France, 48 (1920), 33–94, 208–314 | MR | Zbl

[3] G. Julia, “Mémoire sur l'itération des fonotions rationnlles”, J. Math. Pures et Appl. (8), 1 (1918), 47–245 | Zbl

[4] P. Montel, Normalnye semeistva analiticheskikh funktsii, ONTI, 1936

[5] M. V. Yakobson, “Struktura polinomialnykh otobrazhenii na osobom mnozhestve”, Matem. sb., 77(119) (1968), 105–124 | Zbl

[6] J. F. Ritt, “On the iteration of rational function”, Trans. Amer. Math. Soc., 21:3 (1920), 348–356 | DOI | MR | Zbl

[7] Zh. Valiron, Analiticheskie funktsii, Gostekhizdat, M., 1957

[8] X. K. Kenzhegulov, Iteratsionnye posledovatelnosti vysshikh klassov v veschestvennoi i kompleksnoi oblastyakh, kand. dissertatsiya, Kuibyshev, 1967