Self-similarity and spectral dynamics
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Published:2022-03-15
Issue:1
Volume:87
Page:355-388
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ISSN:0379-4024
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Container-title:Journal of Operator Theory
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language:
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Short-container-title:J. Operator Theory
Author:
Goldberg Bryan, ,Yang Rongwei,
Abstract
This paper investigates a connection between self-similar group representations and induced rational maps on the projective space which preserve the projective spectrum of the group. The focus is on the infinite dihedral group D∞. The main theorem states that the Julia set of the induced rational map F on P2 for D∞ is the union of the projective spectrum with F's extended indeterminacy set. Moreover, the limit function of the iteration sequence {F∘n} on the Fatou set is fully described. This discovery finds an application to the Grigorchuk group G of intermediate growth and its induced rational map G on P4. In the end, the paper proposes the conjecture that G's projective spectrum is contained in the Julia set of G.
Publisher
Theta Foundation
Subject
Algebra and Number Theory
Cited by
1 articles.
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