Constructive Analysis of Iterated Rational Functions
Дата
Авторы
Clark,Jeremy
Journal Title
Journal ISSN
Volume Title
Издатель
Journal of Universal Computer Science
Аннотация
Описание
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.
Ключевые слова
constructive analysis , iteration of rational functions