The spectral problem, substitutions and iterated monodromy

Abstract

We provide a self-similar measure for the self-similar group G acting faithfully on the binary rooted tree, defined as the iterated monodromy group of the quadratic polynomial z + i. We also provide an Lpresentation for G and calculations related to the spectrum of the Markov operator on the Schreier graph of the action of G on the orbit of a point on the boundary of the binary rooted tree.

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Cite this paper

@inproceedings{Grigorchuk2006TheSP, title={The spectral problem, substitutions and iterated monodromy}, author={Rostislav I. Grigorchuk and Dmytro Savchuk and Zoran Sunic and Stanislav Molchanov}, year={2006} }