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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.

MSC:
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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