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Volume 11 / Issue 12

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DOI:   10.3217/jucs-011-12-1904


Constructive Analysis of Iterated Rational Functions

Jeremy Clark (107 rue de Sèvres, France)

Abstract: We develop the elementary theory of iterated rational functions over the Riemann sphere in a constructive setting. We use Bishop­style constructive proof methods throughout. Starting from the development of constructive complex analysis presented in [Bishop and Bridges 1985], we give constructive proofs of Montel's Theorem along with necessary generalisations, and use them to prove elementary facts concerning the Julia set of a general continuous rational function with complex coefficients. We finish with a construction of repelling cycles for these maps, thereby showing that Julia sets are always inhabited.

Keywords: constructive analysis, iteration of rational functions

Categories: F.2.1, G.1.0