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Holomorphic correspondences related to finitely generated rational semigroups

Bharali, Gautam and Sridharan, Shrihari (2017) Holomorphic correspondences related to finitely generated rational semigroups. In: INTERNATIONAL JOURNAL OF MATHEMATICS, 28 (14).

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Official URL: http://dx.doi.org/10.1142/S0129167X17501087

Abstract

In this paper, we present a new technique for studying the dynamics of a finitely generated rational semigroup. Such a semigroup can be associated naturally to a certain holomorphic correspondence on P-1. Results on the iterative dynamics of such a correspondence can now be applied to the study of the rational semigroup. We focus on an invariant measure for the aforementioned correspondence - known as the equilibrium measure. This confers some advantages over many of the known techniques for studying the dynamics of rational semigroups. We use the equilibrium measure to analyze the distribution of repelling fixed points of a finitely generated rational semigroup, and to derive a sharp bound for the Hausdorff dimension of the Julia set of such a semigroup.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the WORLD SCIENTIFIC PUBL CO PTE LTD, 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 20 Jan 2018 06:08
Last Modified: 20 Jan 2018 06:08
URI: http://eprints.iisc.ac.in/id/eprint/58832

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