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Puzzles and para-puzzles of quadratic and cubic polynomials. (English) Zbl 0853.58087
Devaney, Robert L. (ed.), Complex dynamical systems. The mathematics behind the Mandelbrot and Julia sets. Lecture notes prepared for the American Mathematical Society short course, held in Cincinnati, OH, USA, January 10-11, 1994. Providence, RI: American Mathematical Society. Proc. Symp. Appl. Math. 49, 31-69 (1994).
Author’s abstract: “The paper reviews the construction of puzzles of quadratic and cubic polynomials with one bounded critical orbit. The similarities in the constructions are emphasized. In the quadratic case the goal is to prove local connectivity of the Julia set; in the cubic case the goal is to characterize the polynomials with totally disconnected Julia set. The constructions of para-puzzles are also briefly reviewed”.
For the entire collection see [Zbl 0809.00024].
Reviewer: L.Stoyanov (Perth)

37F99 Dynamical systems over complex numbers
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable