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Turning curves for critically recurrent cubic polynomials. (English) Zbl 0963.37040
This paper deals with the classification of turning curves which are a very useful tool to study the parameter spaces for polynomials. The author presents examples which show that it is possible for such a curve to be of finite length. Moreover it is known that the turning curve in the recurrent case can be infinite, for example for so-called Fibonacci polynomials. These polynomials satisfy a stronger condition, known as persistent recurrence. The author also addresses the relation of persistent recurrence to the length of the turning curve.

37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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