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Birkhäuser

Polynomial Automorphisms

and the Jacobian Conjecture

  • Book
  • © 2000

Overview

Authors:
  1. Arno Essen

    1. Department of Mathematics, University of Nijmegen, Nijmegen, The Netherlands

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Part of the book series: Progress in Mathematics (PM, volume 190)

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Table of contents (10 chapters)

  1. Front Matter

    Pages N2-xviii
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  2. Methods

    1. Front Matter

      Pages 1-1
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    2. Preliminaries

      • Arno van den Essen
      Pages 3-42

    3. Derivations and polynomial automorphisms

      • Arno van den Essen
      Pages 43-60

    4. Invertibility criteria and inversion formulae

      • Arno van den Essen
      Pages 61-75

    5. Injective morphisms

      • Arno van den Essen
      Pages 77-84

    6. The tame automorphism group of a polynomial ring

      • Arno van den Essen
      Pages 85-116

    7. Stabilization Methods

      • Arno van den Essen
      Pages 117-141

    8. Polynomial maps with nilpotent Jacobian

      • Arno van den Essen
      Pages 143-171

  3. Applications

    1. Front Matter

      Pages 173-173
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    2. Applications of polynomial mappings to dynamical systems

      • Arno van den Essen
      Pages 175-201

    3. Group actions

      • Arno van den Essen
      Pages 203-237

    4. The Jacobian conjecture

      • Arno van den Essen
      Pages 239-273

  4. Back Matter

    Pages 277-329
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Keywords

About this book

Motivated by some notorious open problems, such as the Jacobian conjecture and the tame generators problem, the subject of polynomial automorphisms has become a rapidly growing field of interest. This book, the first in the field, collects many of the results scattered throughout the literature. It introduces the reader to a fascinating subject and brings him to the forefront of research in this area. Some of the topics treated are invertibility criteria, face polynomials, the tame generators problem, the cancellation problem, exotic spaces, DNA for polynomial automorphisms, the Abhyankar-Moh theorem, stabilization methods, dynamical systems, the Markus-Yamabe conjecture, group actions, Hilbert's 14th problem, various linearization problems and the Jacobian conjecture. The work is essentially self-contained and aimed at the level of beginning graduate students. Exercises are included at the end of each section. At the end of the book there are appendices to cover used material from algebra, algebraic geometry, D-modules and Gröbner basis theory. A long list of ''strong'' examples and an extensive bibliography conclude the book.

Reviews

"…This book is a valuable reference for the study of polynomial automorphisms, due to its breadth of coverage and clarity of exposition."

--Mathematical Reviews

Authors and Affiliations

  • Department of Mathematics, University of Nijmegen, Nijmegen, The Netherlands

    Arno Essen

Bibliographic Information

  • Book Title: Polynomial Automorphisms

  • Book Subtitle: and the Jacobian Conjecture

  • Authors: Arno Essen

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-8440-2

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2000

  • Hardcover ISBN: 978-3-7643-6350-5Published: 01 September 2000

  • Softcover ISBN: 978-3-0348-9567-5Published: 24 October 2012

  • eBook ISBN: 978-3-0348-8440-2Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: XVIII, 329

  • Topics: Algebra

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