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Étude dynamique des polynômes complexes. (Dynamical study of complex polynomials). (French) Zbl 0571.30026

Publ. Math. Orsay 85-04, 138 p. (1984).
These notes complete the program begun in the first part [the authors, ibid. 84-02, 75 p. (1984; Zbl 0552.30018)], that is, an extensive study of Mandelbrot set for the functions \(z^ 2+c\), where c is a complex parameter. In particular, it is shown that the local connectivity of M (still an open question) would imply that the interior of M has a relatively ”simple” structure, consisting of what the authors call ”hyperbolic components”.
Reviewer: I.N.Baker

MSC:

30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
37Cxx Smooth dynamical systems: general theory

Citations:

Zbl 0552.30018