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Fractal Geometry and Stochastics VIThe Continuum Self-Similar Tree

Fractal Geometry and Stochastics VI: The Continuum Self-Similar Tree [We introduce the continuum self-similar tree (CSST) as the attractor of an iterated function system in the complex plane. We provide a topological characterization of the CSST and use this to relate the CSST to other metric trees such as the continuum random tree (CRT) and Julia sets of postcritically-finite polynomials.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Fractal Geometry and Stochastics VIThe Continuum Self-Similar Tree

Part of the Progress in Probability Book Series (volume 76)
Editors: Freiberg, Uta; Hambly, Ben; Hinz, Michael; Winter, Steffen
Bonk, Mario; Tran, Huy
Fractal Geometry and Stochastics VI — Mar 24, 2021
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References (24)

Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2021
ISBN
978-3-030-59648-4
Pages
143 –189
DOI
10.1007/978-3-030-59649-1_7
Publisher site
See Chapter on Publisher Site

Abstract

[We introduce the continuum self-similar tree (CSST) as the attractor of an iterated function system in the complex plane. We provide a topological characterization of the CSST and use this to relate the CSST to other metric trees such as the continuum random tree (CRT) and Julia sets of postcritically-finite polynomials.]

Published: Mar 24, 2021

Keywords: Metric tree; Iterated function system; Continuum random tree; Julia set; Primary: 37C70; Secondary: 37B45

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