The W. Thurston Algorithm for Real Quadratic Rational Maps
Araceli Bonifant, John Milnor, Scott Sutherland
TL;DR
This paper investigates the Thurston algorithm for real quadratic rational maps, focusing on critically finite maps, behavior in obstructed cases, and applications to topological entropy, offering new insights into moduli spaces.
Contribution
It provides a detailed analysis of the Thurston algorithm's behavior in obstructed cases and introduces a new description of relevant moduli spaces for real quadratic maps.
Findings
Effective construction of critically finite maps with specified combinatorics.
Analysis of Thurston algorithm behavior in obstructed and exceptional cases.
Application to understanding topological entropy in real quadratic maps.
Abstract
A study of real quadratic maps with real critical points, emphasizing the effective construction of critically finite maps with specified combinatorics. We discuss the behavior of the Thurston algorithm in obstructed cases, and in one exceptional badly behaved case, and provide a new description of the appropriate moduli spaces. There is also an application to topological entropy.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Cellular Automata and Applications