Description
Book SynopsisPresents the fundamentals of non-archimedean dynamics, including a unified exposition of Rivera-Letelier's classification theorem, as well as results on wandering domains, repelling periodic points, and equilibrium measures. The Berkovich projective line is developed from the ground up, as are relevant results in non-archimedean analysis.
Table of Contents
- Introduction
- Basic dynamics on $\mathbb{P}^1(K)$
- Some background on non-archimedean fields
- Power series and Laurent series
- Fundamentals of non-archimedean dynamics
- Fatou and Julia sets
- The Berkovich projective line
- Rational functions and Berkovich space
- Introduction to dynamics on Berkovich space
- Classifying Berkovich Fatou components
- Further results on periodic components
- Wandering domains
- Repelling points in Berkovich space
- The equilibrium measure
- Proofs of results from non-archimedean analysis
- Proofs of Berkovich space results
- Proofs of results on Berkovich maps
- Fatou components without Berkovich space
- Other constructions of Berkovich spaces
- Bibliography
- Index.
