The real Fatou conjecture (AM-144)

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...

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Detalles Bibliográficos
Autores principales: Graczyk, Jacek, Swiatek, Grzegorz
Lenguaje:eng
Publicado: Princeton University Press 2014
Materias:
Mathematical Physics and Mathematics
Acceso en línea:http://cds.cern.ch/record/1953265
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author Graczyk, Jacek
Swiatek, Grzegorz
author_facet Graczyk, Jacek
Swiatek, Grzegorz
author_sort Graczyk, Jacek
collection CERN
description 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 provi
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institution Organización Europea para la Investigación Nuclear
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publishDate 2014
publisher Princeton University Press
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spelling cern-19532652021-04-21T20:51:55Zhttp://cds.cern.ch/record/1953265engGraczyk, JacekSwiatek, GrzegorzThe real Fatou conjecture (AM-144)Mathematical Physics and Mathematics 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 proviPrinceton University Pressoai:cds.cern.ch:19532652014
spellingShingle Mathematical Physics and Mathematics
Graczyk, Jacek
Swiatek, Grzegorz
The real Fatou conjecture (AM-144)
title The real Fatou conjecture (AM-144)
title_full The real Fatou conjecture (AM-144)
title_fullStr The real Fatou conjecture (AM-144)
title_full_unstemmed The real Fatou conjecture (AM-144)
title_short The real Fatou conjecture (AM-144)
title_sort real fatou conjecture (am-144)
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/1953265
work_keys_str_mv AT graczykjacek therealfatouconjectuream144
AT swiatekgrzegorz therealfatouconjectuream144
AT graczykjacek realfatouconjectuream144
AT swiatekgrzegorz realfatouconjectuream144

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