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Title: Two families of holomorphic correspondences
Author: Curtis, Andrew
ISNI:       0000 0004 5355 3530
Awarding Body: Queen Mary, University of London
Current Institution: Queen Mary, University of London
Date of Award: 2014
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Holomorphic correspondences are multivalued functions from the Riemann sphere to itself. This thesis is concerned with a certain type of holomorphic correspondence known as a covering correspondence. In particular we are concerned with a one complexdimensional family of correspondences constructed by post-composing a covering correspondence with a conformal involution. Correspondences constructed in this manner have varied and intricate dynamics. We introduce and analyze two subfamilies of this parameter space. The first family consists of correspondences for which the limit set is a Cantor set, the second family consists of correspondences for which the limit set is connected and for which the action of the correspondence on the complement of this limit set exhibits certain group like behaviour.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Holomorphic correspondences ; covering correspondence ; Cantor set correspondences ; Klein Combination Theorem ; matings