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Potential theory and dynamics on the Berkovich projective line.


Potential theory and dynamics on the Berkovich projective line.

Baker, Matthew and Robert Rumely.

American Mathematical Society


428 pages



Mathematical surveys and monographs; v.159


This mathematics monograph is presented with a number of goals in mind. The authors develop the foundations of potential theory on the Berkovich projective line, including the definition of a measure-valued Laplacian operator, capacity theory, and a theory of harmonic and subharmonic functions. They also present applications of potential theory on the Berkovcih projective line, especially to the dynamics of rational maps defined over an arbitrary complete and algebraically closed non-Archimedean field K. Finally, they seek to use the case of the Berkovich projective line as a means of introduction to Berkovich's theory of analytic spaces.

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Publication:SciTech Book News
Article Type:Book review
Date:Jun 1, 2010
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