£88.82

Potential Theory and Dynamics on the Berkovich Projective Line (Mathematical Surveys and Monographs)

Biography

Price data last checked 92 day(s) ago - refreshing...

View at Amazon

We'll watch every seller, every day. One email when your price arrives.

About as cheap as it gets. The only time it was cheaper was 10 months ago.

£89 today · all-time low £88 (Jul 2025) · usually the usual

NEW HERE?

Amazon shows you one price. We show you all of them.

Tosheroon watches Amazon prices so you don't have to. Every product on Amazon has a price history — we make it visible. Set the price you'd actually pay, and we'll email you the second it gets there. No app, no account, one email.

WHAT'S ON THIS PAGE

↓ Price chart
when this has been cheap or pricey

↓ Forecast
where the price is heading next

↓ Statistics
all-time high & low, recent range

↑ Price alert
name your number, we'll email you

Price History & Forecast

Grey patches = out of stock. Cheaper = lower on the chart. Hover for exact prices.

Last 639 days • 639 data points (No recent data available)

Historical

Generating forecast...

Price Distribution

Price distribution over 639 days • 6 price levels

Days at Price

Current Price

Price Analysis

Most common price: £110 (230 days, 36.0%)

Price range: £88 - £121

Price levels: 6 different prices over 639 days

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, 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.

Product Specifications

Format: hardcover
ASIN: 0821849247
Category: Books > Subjects > Biography
Domain: Amazon UK
Release Date: 15 March 2010
Listed Since: 30 November 2009

Barcode

No barcode data available

Potential Theory and Dynamics on the Berkovich Projective Line (Mathematical Surveys and Monographs)

About as cheap as it gets. The only time it was cheaper was 10 months ago.

Price History & Forecast

Price Distribution

Price Analysis

Description

Product Specifications

Barcode

Similar Products You Might Like

Advances in Ultrametric Analysis (Contemporary Mathematics)

Classical and Modern Potential Theory and Applications: 430 (Nato Science Series C:, 430)

Classical and Modern Potential Theory and Applications: 430 (Nato Science Series C:, 430)

Complex Analysis and Potential Theory (Crm Proceedings & Lecture Notes)

Lectures on Analytic Differential Equations (Graduate Studies in Mathematics)

Analytic Partial Differential Equations: 359 (Grundlehren der mathematischen Wissenschaften, 359)

Complex Analysis and Dynamical Systems VI: Part 2: Complex Analysis, Quasiconformal Mappings, Complex Dynamics: 6 (Contemporary Mathematics)

Period Functions for Maass Wave Forms and Cohomology (Memoirs of the American Mathematical Society)

Holomorphic Operator Functions of One Variable and Applications: Methods from Complex Analysis in Several Variables: 192 (Operator Theory: Advances and Applications, 192)

Dynamics in One Complex Variable. (AM-160): Third Edition (Annals of Mathematics Studies, 160)

Cambridge Operator Analysis: Hilbert Space Methods in Complex Analysis

Complex Analysis and Geometry (University Series in Mathematics)

A Course in Complex Analysis and Riemann Surfaces (Graduate Studies in Mathematics)

More Explorations in Complex Functions: 298 (Graduate Texts in Mathematics, 298)

Topics in Complex Analysis (Universitext)

Introductory Functional Analysis with Applications: 17 (Wiley Classics Library)

J-holomorphic Curves and Symplectic Topology: Second Edition (American Mathematical Society) (Colloquium Publications)

Introduction to Complex Analytic Geometry

The Cauchy Method of Residues: Theory and Applications: 9 (Mathematics and its Applications, 9)

Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers: 28 (Algorithms and Computation in Mathematics, 28)

Complex Analytic Sets: 46 (Mathematics and its Applications, 46)

Holomorphic Functions and Integral Representations in Several Complex Variables: 108 (Graduate Texts in Mathematics, 108)

Spectral Theory and Analytic Geometry over Non-Archimedean Fields (Mathematical Surveys and Monographs)

Pseudo-Differential Operators, Generalized Functions and Asymptotics: 231 (Operator Theory: Advances and Applications, 231)