Dynamics in one complex variable /:
This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton :
Princeton University Press,
2006.
|
| Ausgabe: | 3rd ed. |
| Schriftenreihe: | Annals of mathematics studies ;
no. 160. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field. |
| Beschreibung: | 1 online resource (viii, 304 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 277-291) and index. |
| ISBN: | 9781400835539 1400835534 1283001489 9781283001489 9786613001481 6613001481 |
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| 245 | 1 | 0 | |a Dynamics in one complex variable / |c by John Milnor. |
| 250 | |a 3rd ed. | ||
| 260 | |a Princeton : |b Princeton University Press, |c 2006. | ||
| 300 | |a 1 online resource (viii, 304 pages) : |b illustrations | ||
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| 490 | 1 | |a Annals of mathematics studies ; |v no. 160 | |
| 504 | |a Includes bibliographical references (pages 277-291) and index. | ||
| 505 | 0 | |a Riemann surfaces -- Iterated holomorphic maps -- Local fixed point theory -- Periodic points: global theory -- Structure of the Fatou set -- Using the Fatou set to study the Julia set. | |
| 588 | 0 | |a Print version record. | |
| 520 | |a This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field. | ||
| 546 | |a In English. | ||
| 650 | 0 | |a Functions of complex variables. |0 http://id.loc.gov/authorities/subjects/sh85052356 | |
| 650 | 0 | |a Holomorphic mappings. |0 http://id.loc.gov/authorities/subjects/sh85061537 | |
| 650 | 0 | |a Riemann surfaces. |0 http://id.loc.gov/authorities/subjects/sh85114044 | |
| 650 | 6 | |a Fonctions d'une variable complexe. | |
| 650 | 6 | |a Applications holomorphes. | |
| 650 | 6 | |a Surfaces de Riemann. | |
| 650 | 7 | |a MATHEMATICS |x Complex Analysis. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a Functions of complex variables |2 fast | |
| 650 | 7 | |a Holomorphic mappings |2 fast | |
| 650 | 7 | |a Riemann surfaces |2 fast | |
| 650 | 7 | |a Iterierte Abbildung |2 gnd |0 http://d-nb.info/gnd/4162626-6 | |
| 650 | 7 | |a Fixpunkttheorie |2 gnd |0 http://d-nb.info/gnd/4293945-8 | |
| 650 | 7 | |a Julia-Menge |2 gnd |0 http://d-nb.info/gnd/4431306-8 | |
| 650 | 7 | |a Fatou-Menge |2 gnd |0 http://d-nb.info/gnd/4414549-4 | |
| 650 | 7 | |a Riemannsche Fläche |2 gnd |0 http://d-nb.info/gnd/4049991-1 | |
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| author | Milnor, John W. (John Willard), 1931- |
| author_GND | http://id.loc.gov/authorities/names/n50033349 |
| author_facet | Milnor, John W. (John Willard), 1931- |
| author_role | |
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| callnumber-raw | QA331.7 .M55 2006eb |
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| callnumber-sort | QA 3331.7 M55 42006EB |
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| classification_rvk | SI 830 |
| collection | ZDB-4-EBA |
| contents | Riemann surfaces -- Iterated holomorphic maps -- Local fixed point theory -- Periodic points: global theory -- Structure of the Fatou set -- Using the Fatou set to study the Julia set. |
| ctrlnum | (OCoLC)704277558 |
| dewey-full | 515/.93 |
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| discipline | Mathematik |
| edition | 3rd ed. |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn704277558 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:17:43Z |
| institution | BVB |
| isbn | 9781400835539 1400835534 1283001489 9781283001489 9786613001481 6613001481 |
| language | English |
| oclc_num | 704277558 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (viii, 304 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Princeton University Press, |
| record_format | marc |
| series | Annals of mathematics studies ; |
| series2 | Annals of mathematics studies ; |
| spelling | Milnor, John W. (John Willard), 1931- https://id.oclc.org/worldcat/entity/E39PBJwMFMhK4jDRHRPTkdm68C http://id.loc.gov/authorities/names/n50033349 Dynamics in one complex variable / by John Milnor. 3rd ed. Princeton : Princeton University Press, 2006. 1 online resource (viii, 304 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Annals of mathematics studies ; no. 160 Includes bibliographical references (pages 277-291) and index. Riemann surfaces -- Iterated holomorphic maps -- Local fixed point theory -- Periodic points: global theory -- Structure of the Fatou set -- Using the Fatou set to study the Julia set. Print version record. This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field. In English. Functions of complex variables. http://id.loc.gov/authorities/subjects/sh85052356 Holomorphic mappings. http://id.loc.gov/authorities/subjects/sh85061537 Riemann surfaces. http://id.loc.gov/authorities/subjects/sh85114044 Fonctions d'une variable complexe. Applications holomorphes. Surfaces de Riemann. MATHEMATICS Complex Analysis. bisacsh MATHEMATICS General. bisacsh Functions of complex variables fast Holomorphic mappings fast Riemann surfaces fast Iterierte Abbildung gnd http://d-nb.info/gnd/4162626-6 Fixpunkttheorie gnd http://d-nb.info/gnd/4293945-8 Julia-Menge gnd http://d-nb.info/gnd/4431306-8 Fatou-Menge gnd http://d-nb.info/gnd/4414549-4 Riemannsche Fläche gnd http://d-nb.info/gnd/4049991-1 Holomorphe Abbildung gnd http://d-nb.info/gnd/4160471-4 Academic Search Complete EBSCO Print version: Milnor, John W. (John Willard), 1931- Dynamics in one complex variable. 3rd ed. Princeton : Princeton University Press, 2006 0691124876 (DLC) 2005051060 (OCoLC)60791765 Annals of mathematics studies ; no. 160. http://id.loc.gov/authorities/names/n42002129 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=356986 Volltext |
| spellingShingle | Milnor, John W. (John Willard), 1931- Dynamics in one complex variable / Annals of mathematics studies ; Riemann surfaces -- Iterated holomorphic maps -- Local fixed point theory -- Periodic points: global theory -- Structure of the Fatou set -- Using the Fatou set to study the Julia set. Functions of complex variables. http://id.loc.gov/authorities/subjects/sh85052356 Holomorphic mappings. http://id.loc.gov/authorities/subjects/sh85061537 Riemann surfaces. http://id.loc.gov/authorities/subjects/sh85114044 Fonctions d'une variable complexe. Applications holomorphes. Surfaces de Riemann. MATHEMATICS Complex Analysis. bisacsh MATHEMATICS General. bisacsh Functions of complex variables fast Holomorphic mappings fast Riemann surfaces fast Iterierte Abbildung gnd http://d-nb.info/gnd/4162626-6 Fixpunkttheorie gnd http://d-nb.info/gnd/4293945-8 Julia-Menge gnd http://d-nb.info/gnd/4431306-8 Fatou-Menge gnd http://d-nb.info/gnd/4414549-4 Riemannsche Fläche gnd http://d-nb.info/gnd/4049991-1 Holomorphe Abbildung gnd http://d-nb.info/gnd/4160471-4 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85052356 http://id.loc.gov/authorities/subjects/sh85061537 http://id.loc.gov/authorities/subjects/sh85114044 http://d-nb.info/gnd/4162626-6 http://d-nb.info/gnd/4293945-8 http://d-nb.info/gnd/4431306-8 http://d-nb.info/gnd/4414549-4 http://d-nb.info/gnd/4049991-1 http://d-nb.info/gnd/4160471-4 |
| title | Dynamics in one complex variable / |
| title_auth | Dynamics in one complex variable / |
| title_exact_search | Dynamics in one complex variable / |
| title_full | Dynamics in one complex variable / by John Milnor. |
| title_fullStr | Dynamics in one complex variable / by John Milnor. |
| title_full_unstemmed | Dynamics in one complex variable / by John Milnor. |
| title_short | Dynamics in one complex variable / |
| title_sort | dynamics in one complex variable |
| topic | Functions of complex variables. http://id.loc.gov/authorities/subjects/sh85052356 Holomorphic mappings. http://id.loc.gov/authorities/subjects/sh85061537 Riemann surfaces. http://id.loc.gov/authorities/subjects/sh85114044 Fonctions d'une variable complexe. Applications holomorphes. Surfaces de Riemann. MATHEMATICS Complex Analysis. bisacsh MATHEMATICS General. bisacsh Functions of complex variables fast Holomorphic mappings fast Riemann surfaces fast Iterierte Abbildung gnd http://d-nb.info/gnd/4162626-6 Fixpunkttheorie gnd http://d-nb.info/gnd/4293945-8 Julia-Menge gnd http://d-nb.info/gnd/4431306-8 Fatou-Menge gnd http://d-nb.info/gnd/4414549-4 Riemannsche Fläche gnd http://d-nb.info/gnd/4049991-1 Holomorphe Abbildung gnd http://d-nb.info/gnd/4160471-4 |
| topic_facet | Functions of complex variables. Holomorphic mappings. Riemann surfaces. Fonctions d'une variable complexe. Applications holomorphes. Surfaces de Riemann. MATHEMATICS Complex Analysis. MATHEMATICS General. Functions of complex variables Holomorphic mappings Riemann surfaces Iterierte Abbildung Fixpunkttheorie Julia-Menge Fatou-Menge Riemannsche Fläche Holomorphe Abbildung |
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| work_keys_str_mv | AT milnorjohnw dynamicsinonecomplexvariable |