Linear Chaos

  • Karl-G. Grosse-Erdmann
  • Alfred Peris Manguillot
Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Introduction to linear dynamics

    1. Front Matter
      Pages 1-1
    2. Karl-G. Grosse-Erdmann, Alfred Peris Manguillot
      Pages 3-30
    3. Karl-G. Grosse-Erdmann, Alfred Peris Manguillot
      Pages 31-67
    4. Karl-G. Grosse-Erdmann, Alfred Peris Manguillot
      Pages 69-88
    5. Karl-G. Grosse-Erdmann, Alfred Peris Manguillot
      Pages 89-135
    6. Karl-G. Grosse-Erdmann, Alfred Peris Manguillot
      Pages 137-160
    7. Karl-G. Grosse-Erdmann, Alfred Peris Manguillot
      Pages 161-178
  3. Selected topics

    1. Front Matter
      Pages 179-179
    2. Karl-G. Grosse-Erdmann, Alfred Peris Manguillot
      Pages 181-211
    3. Karl-G. Grosse-Erdmann, Alfred Peris Manguillot
      Pages 213-233
    4. Karl-G. Grosse-Erdmann, Alfred Peris Manguillot
      Pages 235-266
    5. Karl-G. Grosse-Erdmann, Alfred Peris Manguillot
      Pages 267-303
    6. Karl-G. Grosse-Erdmann, Alfred Peris Manguillot
      Pages 305-330
    7. Karl-G. Grosse-Erdmann, Alfred Peris Manguillot
      Pages 331-350
  4. Back Matter
    Pages 351-386

About this book

Introduction

It is commonly believed that chaos is linked to non-linearity, however many (even quite natural) linear dynamical systems exhibit chaotic behavior. The study of these systems is a young and remarkably active field of research, which has seen many landmark results over the past two decades. Linear dynamics lies at the crossroads of several areas of mathematics including operator theory, complex analysis, ergodic theory and partial differential equations. At the same time its basic ideas can be easily understood by a wide audience.

Written by two renowned specialists, Linear Chaos provides a welcome introduction to this theory. Split into two parts, part I presents a self-contained introduction to the dynamics of linear operators, while part II covers selected, largely independent topics from linear dynamics.  More than 350 exercises and many illustrations are included, and each chapter contains a further ‘Sources and Comments’ section.

The only prerequisites are a familiarity with metric spaces, the basic theory of Hilbert and Banach spaces and fundamentals of complex analysis. More advanced tools, only needed occasionally, are provided in two appendices.

A self-contained exposition, this book will be suitable for self-study and will appeal to advanced undergraduate or beginning graduate students. It will also be of use to researchers in other areas of mathematics such as partial differential equations, dynamical systems and ergodic theory.

Keywords

Chaos Dynamical systems Hypercyclicity Linear Operators

Authors and affiliations

  • Karl-G. Grosse-Erdmann
    • 1
  • Alfred Peris Manguillot
    • 2
  1. 1.Institut de MathématiqueUniversité de MonsMonsBelgium
  2. 2.Institut de Matemàtica Pura i AplicadaUniversitat Politècnica de ValènciaValènciaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-2170-1
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-2169-5
  • Online ISBN 978-1-4471-2170-1
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book