View in EDS PDF Full Text

The Real Fatou Conjecture

Saved in:
Bibliographic Details
Title: The Real Fatou Conjecture
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 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.
Authors: Jacek Graczyk, Grzegorz Swiatek
Resource Type: eBook.
Subjects: Geodesics (Mathematics), Mappings (Mathematics), Polynomials
Categories: MATHEMATICS / Geometry / Non-Euclidean, MATHEMATICS / Complex Analysis
Database: eBook Collection (EBSCOhost)
FullText Links:
  – Type: ebook-pdf
Text:
  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 818439
RelevancyScore: 959
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 959.155151367188
IllustrationInfo
ImageInfo – Size: thumb
  Target: https://rps2images.ebscohost.com/rpsweb/othumb?id=NL$818439$PDF&s=r
– Size: medium
  Target: https://rps2images.ebscohost.com/rpsweb/othumb?id=NL$818439$PDF&s=d
Items – Name: Title
  Label: Title
  Group: Ti
  Data: The Real Fatou Conjecture
– Name: Abstract
  Label: Description
  Group: Ab
  Data: 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.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Jacek+Graczyk%22">Jacek Graczyk</searchLink><br /><searchLink fieldCode="AR" term="%22Grzegorz+Swiatek%22">Grzegorz Swiatek</searchLink>
– Name: TypePub
  Label: Resource Type
  Group: TypPub
  Data: eBook.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Geodesics+%28Mathematics%29%22">Geodesics (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mappings+%28Mathematics%29%22">Mappings (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink>
– Name: SubjectBISAC
  Label: Categories
  Group: Su
  Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Geometry+%2F+Non-Euclidean%22">MATHEMATICS / Geometry / Non-Euclidean</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Complex+Analysis%22">MATHEMATICS / Complex Analysis</searchLink>
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=nlebk&AN=818439
RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 516.362
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Geodesics (Mathematics)
        Type: general
      – SubjectFull: Mappings (Mathematics)
        Type: general
      – SubjectFull: Polynomials
        Type: general
    Titles:
      – TitleFull: The Real Fatou Conjecture
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Jacek Graczyk
      – PersonEntity:
          Name:
            NameFull: Grzegorz Swiatek
      – PersonEntity:
          Name:
            NameFull: Jacek Graczyk
      – PersonEntity:
          Name:
            NameFull: Grzegorz Swiatek
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 1998
            – D: 08
              M: 09
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9780691002583
            – Type: isbn-print
              Value: 9780691002576
            – Type: isbn-electronic
              Value: 9781400865185
          Numbering:
            – Type: volume
              Value: 00144
          Titles:
            – TitleFull: The Real Fatou Conjecture
              Type: main
ResultId 1