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A computer-assisted proof of universality for area-preserving maps

About this Title

J.-P. Eckmann, H. Koch and P. Wittwer

Publication: Memoirs of the American Mathematical Society
Publication Year: 1984; Volume 47, Number 289
ISBNs: 978-0-8218-2289-0 (print); 978-1-4704-0699-8 (online)
DOI: https://doi.org/10.1090/memo/0289
MathSciNet review: 727816
MSC: Primary 58F19; Secondary 58F05, 58F14, 65J15

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Table of Contents

Chapters

  • Introduction
  • Part I. Analysis of doubling
  • 1. Feigenbaum universality for area-preserving maps
  • 2. Generating functions
  • 3. Further reduction of the problem
  • 4. Spectral properties
  • 5. Construction of the operator $\mathcal {L}$
  • 6. Construction of the doubling operator
  • Part II. Functional analysis on the computer
  • 1. Interval and neighborhood arithmetics
  • 2. Spectral theory
  • 3. Interval and neighborhood arithmetics on a computer
  • List of correspondence
  • Part III. Proofs
  • 1. Computer program
  • 2. Program output