# Potential Theory and Dynamics on the Berkovich Projective Line

### About this Title

**Matthew Baker**, *Georgia Institute of Technology, Atlanta, GA* and **Robert Rumely**, *University of Georgia, Athens, GA*

Publication: Mathematical Surveys and Monographs

Publication Year:
2010; Volume 159

ISBNs: 978-0-8218-4924-8 (print); 978-1-4704-1386-6 (online)

DOI: https://doi.org/http://dx.doi.org/10.1090/surv/159

MathSciNet review: MR2599526

MSC: Primary 37P50; Secondary 14G20, 14G22, 31C15, 31C45, 37P40

### Table of Contents

**Front/Back Matter**

**Chapters**

- 1. The Berkovich unit disc
- 2. The Berkovich projective line
- 3. Metrized graphs
- 4. The Hsia kernel
- 5. The Laplacian on the Berkovich projective line
- 6. Capacity theory
- 7. Harmonic functions
- 8. Subharmonic functions
- 9. Multiplicities
- 10. Applications to the dynamics of rational maps
- 11. Some results from analysis and topology
- 12. $\mathbb {R}$-trees and Gromov hyperbolicity
- 13. Brief overview of Berkovich’s theory