JUCS - Journal of Universal Computer Science 11(12): 1904-1931, doi: 10.3217/jucs-011-12-1904
Constructive Analysis of Iterated Rational Functions
expand article infoJeremy Clark
‡ 107 rue de Sevres, Paris, France
Open Access
We develop the elementary theory of iterated rational functions over the Riemann sphere in a constructive setting. We use Bishop style 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.
constructive analysis, iteration of rational functions