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Frontiers in Complex DynamicsIn Celebration of John Milnor's 80th Birthday$
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Araceli Bonifant, Misha Lyubich, and Scott Sutherland

Print publication date: 2014

Print ISBN-13: 9780691159294

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159294.001.0001

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Arithmetic of Unicritical Polynomial Maps

Arithmetic of Unicritical Polynomial Maps

Chapter:
(p.16) (p.15) Arithmetic of Unicritical Polynomial Maps
Source:
Frontiers in Complex Dynamics
Author(s):

John Milnor

, Araceli Bonifant, Mikhail Lyubich, Scott Sutherland
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159294.003.0002

This chapter studies complex polynomials with only one critical point, relating arithmetic properties of the coefficients to those of periodic orbits and their multipliers and external rays. It first defines the complex polynomial maps of degree n ≥ 2, and draws an alternate normal form for studying periodic orbits. The chapter also discusses the notation for the integral closure. Next, the chapter discusses several statements about periodic orbits. It then proceeds to lay out the proofs of these statements, in the process detailing some basic properties of the integral closure. Finally, the chapter closes with a discussion of the critically finite case.

Keywords:   complex polynomials, unicritical polynomial maps, critical point, periodic orbits, integral closure, critically finite case

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