Regular and limit sets for holomorphic correspondences

• Autorzy: S. Bullett , C. Penrose
• Języki publikacji: EN

Abstrakty

EN

Holomorphic correspondences are multivalued maps $f = Q̃₊Q̃₋^{-1}: Z → W$ between Riemann surfaces Z and W, where Q̃₋ and Q̃₊ are (single-valued) holomorphic maps from another Riemann surface X onto Z and W respectively. When Z = W one can iterate f forwards, backwards or globally (allowing arbitrarily many changes of direction from forwards to backwards and vice versa). Iterated holomorphic correspondences on the Riemann sphere display many of the features of the dynamics of Kleinian groups and rational maps, of which they are a generalization. We lay the foundations for a systematic study of regular and limit sets for holomorphic correspondences, and prove theorems concerning the structure of these sets applicable to large classes of such correspondences.

Kategorie tematyczne

• 30D05: Functional equations in the complex domain, iteration and composition of analytic functions
• 30F40: Kleinian groups
• 37F05: Relations and correspondences

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 167
• Numer: 2
• Strony: 111-171

Daty

wydano

2001

Twórcy

autor

S. Bullett

• School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS, UK

autor

C. Penrose

• School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS, UK

Identyfikatory

DOI

10.4064/fm167-2-2