Exponential growth of some iterated monodromy groups

Hlushchanka, Mikhail and Meyer, Daniel (2018) Exponential growth of some iterated monodromy groups. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 116 (6). pp. 1489-1518.

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Abstract

Iterated monodromy groups of postcritically finite rational maps form a rich class of self‐similar groups with interesting properties. There are examples of such groups that have intermediate growth, as well as examples that have exponential growth. These groups arise from polynomials. We show exponential growth of the IMG of several non‐polynomial maps. These include rational maps whose Julia set is the whole sphere, rational maps with Sierpiński carpet Julia set, and obstructed Thurston maps. Furthermore, we construct the first example of a non‐renormalizable polynomial with a dendrite Julia set whose IMG has exponential growth.

Item Type:	Article
Additional Information:	39 pages, 12 figures
Uncontrolled Keywords:	37F10, 37F25 (primary), 20E08 (secondary)
Depositing User:	Symplectic Admin
Date Deposited:	21 Dec 2017 09:48
Last Modified:	27 Jan 2023 02:52
DOI:	10.1112/plms.12118
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3014260