The Real Fatou Conjecture
eBook - PDF

The Real Fatou Conjecture

  1. 158 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

The Real Fatou Conjecture

About this book

In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it can be interpreted to mean that for a dense set of parameters "a," an attracting periodic orbit exists. The same question appears naturally in science, where the logistic family is used to construct models in physics, ecology, and economics.


In this book, Jacek Graczyk and Grzegorz Swiatek provide a rigorous proof of the Real Fatou Conjecture. In spite of the apparently elementary nature of the problem, its solution requires advanced tools of complex analysis. The authors have written a self-contained and complete version of the argument, accessible to someone with no knowledge of complex dynamics and only basic familiarity with interval maps. The book will thus be useful to specialists in real dynamics as well as to graduate students.

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Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. Contents
  6. 1 Review of Concepts
  7. 2 Quasiconformal Gluing
  8. 3 Polynomial-Like Property
  9. 4 Linear Growth of Moduli
  10. 5 Quasiconformal Techniques
  11. Bibliography
  12. Index

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Yes, you can access The Real Fatou Conjecture by Jacek Graczyk,Grzegorz Swiatek in PDF and/or ePUB format, as well as other popular books in Mathematics & Complex Analysis. We have over one million books available in our catalogue for you to explore.