Potential Theory and Dynamics on the Berkovich Projective Line (Mathematical Surveys and Monographs Series), Vol. 159

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PThe 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#151;on analysis, $\mathbb{R}$-trees, and Berkovich's general theory of analytic spaces#151;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 resultssuch as the Fekete-Szego theorem and Bilu's equidistribution theorem.

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بستن

فرمت کتاب

ebook

زبان

english

تاریخ انتشار

2010

نویسنده

Matthew Baker

ناشر

American Mathematical Society

شابک

9780821849248

20,000 تومان

خرید کتاب مطالعه نمونه درخواست ترجمه کتاب

خرید کتاب Potential Theory and Dynamics on the Berkovich Projective Line (Mathematical Surveys and Monographs Series), Vol. 159

Potential Theory and Dynamics on the Berkovich Projective Line (Mathematical Surveys and Monographs Series), Vol. 159

گزارش تخلف

فرمت کتاب

ebook

زبان

english

تاریخ انتشار

2010

نویسنده

ناشر

شابک

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