Thuston's Teapots and Graph Directed Systems
Chenxi Wu
TL;DR
This paper explores the geometric structure of Thurston's Master Teapot, linking it to the Mandelbrot set of graph directed iterated function systems, and reveals its significance in understanding entropies of unimodal maps.
Contribution
It establishes a novel connection between Thurston's Master Teapot and the Mandelbrot set of graph directed systems, enhancing the understanding of entropy in dynamical systems.
Findings
Connected Thurston's Master Teapot to Mandelbrot set of graph systems
Provided new insights into entropies of unimodal maps
Extended the geometric understanding of dynamical systems
Abstract
Thurston's Master Teapot is a geometric object that encodes the entropies of critically periodic unimodal maps. We establish the connection between this object and the "Mandelbrot set" of graph directed iterated function systems previously studied by Solomyak.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Cellular Automata and Applications · Quasicrystal Structures and Properties