# Regular and limit sets for holomorphic correspondences

Fundamenta Mathematicae (2001)

- Volume: 167, Issue: 2, page 111-171
- ISSN: 0016-2736

## Access Full Article

top## Abstract

top## How to cite

topS. Bullett, and C. Penrose. "Regular and limit sets for holomorphic correspondences." Fundamenta Mathematicae 167.2 (2001): 111-171. <http://eudml.org/doc/282042>.

@article{S2001,

abstract = {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.},

author = {S. Bullett, C. Penrose},

journal = {Fundamenta Mathematicae},

keywords = {holomorphic dynamics; correspondences; regular sets; limit sets},

language = {eng},

number = {2},

pages = {111-171},

title = {Regular and limit sets for holomorphic correspondences},

url = {http://eudml.org/doc/282042},

volume = {167},

year = {2001},

}

TY - JOUR

AU - S. Bullett

AU - C. Penrose

TI - Regular and limit sets for holomorphic correspondences

JO - Fundamenta Mathematicae

PY - 2001

VL - 167

IS - 2

SP - 111

EP - 171

AB - 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.

LA - eng

KW - holomorphic dynamics; correspondences; regular sets; limit sets

UR - http://eudml.org/doc/282042

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.