The real Fatou conjecture:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[1998]
|
| Schriftenreihe: | Annals of Mathematics Studies
144 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (148p.) |
| ISBN: | 9781400865185 |
| DOI: | 10.1515/9781400865185 |
Internformat
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| 490 | 1 | |a Annals of Mathematics Studies |v number 144 | |
| 500 | |a 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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Datensatz im Suchindex
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| author | Graczyk, Jacek Świa̧tek, Grzegorz 1964- |
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| author_facet | Graczyk, Jacek Świa̧tek, Grzegorz 1964- |
| author_role | aut aut |
| author_sort | Graczyk, Jacek |
| author_variant | j g jg g ś gś |
| building | Verbundindex |
| bvnumber | BV042524175 |
| classification_rvk | SI 830 SK 350 |
| collection | ZDB-23-DGG ZDB-23-PST |
| ctrlnum | (OCoLC)887499708 (DE-599)BVBBV042524175 |
| dewey-full | 516.362 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.362 |
| dewey-search | 516.362 |
| dewey-sort | 3516.362 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400865185 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:24:04Z |
| institution | BVB |
| isbn | 9781400865185 |
| language | English |
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| series | Annals of Mathematics Studies |
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| spelling | Graczyk, Jacek aut The real Fatou conjecture Jacek Graczyk, Grzegorz Swiatek Princeton, N.J. Princeton University Press [1998] © 1998 1 Online-Ressource (148p.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 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 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 In English Mathematik Geodesics (Mathematics) Mappings (Mathematics) Polynomials MATHEMATICS / Geometry / General MATHEMATICS / Complex Analysis bisacsh Polynom (DE-588)4046711-9 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Polynom (DE-588)4046711-9 s 1\p DE-604 Świa̧tek, Grzegorz 1964- (DE-588)173129986 aut Erscheint auch als Druck-Ausgabe 0-691-00257-6 Annals of Mathematics Studies 144 (DE-604)BV040389493 144 https://doi.org/10.1515/9781400865185?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Graczyk, Jacek Świa̧tek, Grzegorz 1964- The real Fatou conjecture Annals of Mathematics Studies Mathematik Geodesics (Mathematics) Mappings (Mathematics) Polynomials MATHEMATICS / Geometry / General MATHEMATICS / Complex Analysis bisacsh Polynom (DE-588)4046711-9 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4046711-9 (DE-588)4012248-7 |
| title | The real Fatou conjecture |
| title_auth | The real Fatou conjecture |
| title_exact_search | The real Fatou conjecture |
| title_full | The real Fatou conjecture Jacek Graczyk, Grzegorz Swiatek |
| title_fullStr | The real Fatou conjecture Jacek Graczyk, Grzegorz Swiatek |
| title_full_unstemmed | The real Fatou conjecture Jacek Graczyk, Grzegorz Swiatek |
| title_short | The real Fatou conjecture |
| title_sort | the real fatou conjecture |
| topic | Mathematik Geodesics (Mathematics) Mappings (Mathematics) Polynomials MATHEMATICS / Geometry / General MATHEMATICS / Complex Analysis bisacsh Polynom (DE-588)4046711-9 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Mathematik Geodesics (Mathematics) Mappings (Mathematics) Polynomials MATHEMATICS / Geometry / General MATHEMATICS / Complex Analysis Polynom Differentialgeometrie |
| url | https://doi.org/10.1515/9781400865185?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT graczykjacek therealfatouconjecture AT swiatekgrzegorz therealfatouconjecture |