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