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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
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