Heights of Polynomials and Entropy in Algebraic Dynamics

  • Graham Everest
  • Thomas Ward

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Graham Everest, Thomas Ward
    Pages 1-28
  3. Graham Everest, Thomas Ward
    Pages 29-50
  4. Graham Everest, Thomas Ward
    Pages 51-80
  5. Graham Everest, Thomas Ward
    Pages 81-90
  6. Graham Everest, Thomas Ward
    Pages 91-116
  7. Graham Everest, Thomas Ward
    Pages 117-144
  8. Back Matter
    Pages 145-212

About this book

Introduction

Arithmetic geometry and algebraic dynamical systems are flourishing areas of mathematics. Both subjects have highly technical aspects, yet both of­ fer a rich supply of down-to-earth examples. Both have much to gain from each other in techniques and, more importantly, as a means for posing (and sometimes solving) outstanding problems. It is unlikely that new graduate students will have the time or the energy to master both. This book is in­ tended as a starting point for either topic, but is in content no more than an invitation. We hope to show that a rich common vein of ideas permeates both areas, and hope that further exploration of this commonality will result. Central to both topics is a notion of complexity. In arithmetic geome­ try 'height' measures arithmetical complexity of points on varieties, while in dynamical systems 'entropy' measures the orbit complexity of maps. The con­ nections between these two notions in explicit examples lie at the heart of the book. The fundamental objects which appear in both settings are polynomi­ als, so we are concerned principally with heights of polynomials. By working with polynomials rather than algebraic numbers we avoid local heights and p-adic valuations.

Keywords

Prime algebra calculus nonlinear dynamics number theory

Authors and affiliations

  • Graham Everest
    • 1
  • Thomas Ward
    • 1
  1. 1.School of MathematicsUniversity of East AngliaNorwichUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-3898-3
  • Copyright Information Springer-Verlag London 1999
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-84996-854-6
  • Online ISBN 978-1-4471-3898-3
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book
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