How Long to Read Potential Theory and Dynamics on the Berkovich Projective Line

How Long Does it Take to Read Potential Theory and Dynamics on the Berkovich Projective Line?

It takes the average reader 7 hours and 57 minutes to read Potential Theory and Dynamics on the Berkovich Projective Line by Matthew Baker

Assuming a reading speed of 250 words per minute. Learn more

Description

The purpose of this book is to develop the foundations of potential theory and rational dynamics on the Berkovich projective line over an arbitrary complete, algebraically closed non-Archimedean field. In addition to providing a concrete and ``elementary'' introduction to Berkovich analytic spaces and to potential theory and rational iteration on the Berkovich line, the book contains applications to arithmetic geometry and arithmetic dynamics. A number of results in the book are new, and most have not previously appeared in book form. Three appendices--on analysis, $\mathbb{R}$-trees, and Berkovich's general theory of analytic spaces--are included to make the book as self-contained as possible. The authors first give a detailed description of the topological structure of the Berkovich projective line and then introduce the Hsia kernel, the fundamental kernel for potential theory. Using the theory of metrized graphs, they define a Laplacian operator on the Berkovich line and construct theories of capacities, harmonic and subharmonic functions, and Green's functions, all of which are strikingly similar to their classical complex counterparts. After developing a theory of multiplicities for rational functions, they give applications to non-Archimedean dynamics, including local and global equidistribution theorems, fixed point theorems, and Berkovich space analogues of many fundamental results from the classical Fatou-Julia theory of rational iteration. They illustrate the theory with concrete examples and exposit Rivera-Letelier's results concerning rational dynamics over the field of $p$-adic complex numbers. They also establish Berkovich space versions of arithmetic results such as the Fekete-Szego theorem and Bilu's equidistribution theorem.

How long is Potential Theory and Dynamics on the Berkovich Projective Line?

Potential Theory and Dynamics on the Berkovich Projective Line by Matthew Baker is 466 pages long, and a total of 119,296 words.

This makes it 157% the length of the average book. It also has 146% more words than the average book.

How Long Does it Take to Read Potential Theory and Dynamics on the Berkovich Projective Line Aloud?

The average oral reading speed is 183 words per minute. This means it takes 10 hours and 51 minutes to read Potential Theory and Dynamics on the Berkovich Projective Line aloud.

What Reading Level is Potential Theory and Dynamics on the Berkovich Projective Line?

Potential Theory and Dynamics on the Berkovich Projective Line is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Potential Theory and Dynamics on the Berkovich Projective Line?

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