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Wednesday, May 20, 2020 | History

3 edition of Potential theory and dynamics on the Berkovich projective line found in the catalog.

Potential theory and dynamics on the Berkovich projective line

Matthew Baker

Potential theory and dynamics on the Berkovich projective line

by Matthew Baker

  • 150 Want to read
  • 35 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Potential theory (Mathematics),
  • Topological spaces,
  • Topological dynamics

  • Edition Notes

    Includes bibliographical references and index.

    StatementMatthew Baker, Robert Rumely.
    SeriesMathematical surveys and monographs -- v. 159
    ContributionsRumely, Robert S.
    Classifications
    LC ClassificationsQA404.7 .B35 2010
    The Physical Object
    Paginationp. cm.
    ID Numbers
    Open LibraryOL23713015M
    ISBN 109780821849248
    LC Control Number2009036372
    OCLC/WorldCa436866923

      M. Baker, R. Rumely, Potential Theory and Dynamics on the Berkovich Projective Line. Mathematical Surveys and Monographs, vol. (American Mathematical Society, Providence, RI, ) Google Scholar [Ber]Cited by: 5. Dynamics of Transcendental Entire Maps on Berkovich Affine Line Article in Journal of Dynamics and Differential Equations 25(1) March with 24 Reads How we measure 'reads'.

    Potential theory and dynamics on the Berkovich projective line. By Matthew Baker and Robert Rumely. Topics: Mathematical Physics and Mathematics. Publisher: American Mathematical Society. Year: OAI identifier: oai: Provided by: Author: Matthew Baker and Robert Rumely. From the viewpoint of dynamics and potential theory on the Berkovich projective line, we give a characterization of polynomials among rational functions, up to rational functions having Author: Mattias Jonsson.

    Abstract. This is a set of expanded lecture notes from the Berkovich Space seminar held at the University of Georgia during Spring, The purpose of the notes is to provide a non-technical introduction to Berkovich spaces, and to develop the foundations for analysis on the Berkovich projective line, with a view toward applications in : Robert Rumely and Matthew Baker. Psychoanalysis as Therapy and Storytelling (The New Library of Psychoanalysis) Rosamond Lehmann Potential Theory and Dynamics on the Berkovich Projective Line (Mathematical Surveys and Monographs) HOME.


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Potential theory and dynamics on the Berkovich projective line by Matthew Baker Download PDF EPUB FB2

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 by: This book is a revised and expanded version of the authors’ manuscript \Analysis and Dynamics on the Berkovich Projective Line" ([74], July ).

Its purpose is to develop the foundations of potential theory on the Berkovich projective line P1 Berk over an arbitrary complete, algebraically closed nonar-chimedean Size: 1MB. 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.

Potential Theory and Dynamics on. the Berkovich Projective Line. Matthew Baker. Robert Rumely. This is a preliminary version of the book Potential Theory and Dynamics on the Berkovich Projective Line published by the American Mathematical Society (AMS).

This preliminary version is. 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 Volume ISBNs: (print); (online). Potential Theory and Dynamics on the Berkovich Projective Line Matthew Baker and Robert Rumely Publication Year: ISBN ISBN Mathematical Surveys and Monographs, vol. Its purpose is to develop the foundations of potential theory and rational dynamicsontheBerkovichprojectiveline.

The theory developed here has applications in arithmetic geometry, arithmetic intersection theory, and arithmetic dynamics. In an effort to createareferencewhichisasusefulaspossible,weworkoveranarbitrary. Destination page number Search scope Search Text.

Additional Sources for Math Book Reviews; About MAA Reviews; Mathematical Communication; Information for Libraries; Author Resources; Advertise with MAA; Meetings.

MAA MathFest. Register Now; Registration Rates and Other Fees; Exhibitors and Sponsors; Abstracts; Chronological Schedule; Mathematical Sessions. Invited Addresses; Invited Paper. In addition to providing a concrete introduction to Berkovich’s analytic spaces and to potential theory and rational dynamics on P1Berk, the theory developed here has applications in arithmetic geometry, arithmetic intersection theory, and arithmetic dynamics.

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.

rational functions of degree > 1 on the projective line over an alge-braically closed field that is complete with respect to a non-trivial and non-archimedean absolute value, from the viewpoint of dynamics and potential theory on the Berkovich projective line.

Introduction Let K be an algebraically closed field that is complete with respect to. projective line, with a view toward applications in dynamics. After de-scribing the underlying topological space and the sheaf of functions on the Berkovich line, we introduce the Hsia kernel, the fundamental kernel for potential theory.

We develop a theory of capacities, define a Lapla-cian operator, and construct a theory of harmonic functions. Abstract: This is a set of expanded lecture notes from the Berkovich Space seminar held at the University of Georgia during Spring, The purpose of the notes is to provide a non-technical introduction to Berkovich spaces, and to develop the foundations for analysis on the Berkovich projective line, with a view toward applications in by: Potential theory and dynamics on the Berkovich projective line.

[Matthew Baker; Robert S Rumely] -- 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.

Potential Theory and Dynamics on the Berkovich Projective Line: : Matthew Baker, Robert Rumely: Libri in altre lingueAuthor: Matthew Baker. Baker, Matthew; Rumely, Robert (), Potential theory and dynamics on the Berkovich projective line, Mathematical Surveys and Monographs,Providence, R.I.: American Mathematical Society, ISBNMR Abstract.

Key words and phrases. Berkovich analytic spaces, Berkovich projective line, nonarchimedean geometry, R-trees, metrized graphs, potential theory, Laplacian, capacities, harmonic and subharmonic functions, Green’s functions, Fekete-Szego ̈ theorem, iteration of rational maps, Fatou and Julia sets, canonical heights, equidistribution theorems Contents Preface ix History x Related.

4 4. POTENTIAL THEORY ON BERKOVICH CURVES One obtains the Berkovich projective line P1 Berk by adjoining to A 1 Berk in a suitable manner a point at in nity; the resulting space P1 Berk is a compact, Hausdor, and path-connected topological space which contains P1(K) (with its natural topology) as a dense subspace.

Abstract. This is a set of expanded lecture notes from the Berkovich Space seminar held at the University of Georgia during Spring, The purpose of the notes is to provide a non-technical introduction to Berkovich spaces, and to develop the foundations for analysis on the Berkovich projective line, with a view toward applications in dynamics.

Title: Potential Theory and Dynamics on the Berkovich Projective Line Publication Year: Series: Mathematical Surveys and Monographs, vol. Author: John T. Baldwin Title: Categoricity Publication Year: Series:University Lecture Series, vol. Author: Gregory V. Bard Title: Sage for Undergraduates Publication Year: 4 4.

POTENTIAL THEORY ON BERKOVICH CURVES One obtains the Berkovich projective line P1 Berk by adjoining to A 1 Berk in a suitable manner a point at infinity; the resulting space P1 Berk is a compact, Hausdorff, and path-connected topological space which contains P1(K) (with its natural topology) as a dense subspace.Potential theory and dynamics on the Berkovich projective line.

Providence, R.I.: American Mathematical Society, © (DLC) (OCoLC) Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / .