Complex dynamics and renormalization:
Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely reno...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[1995]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 135 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) |
| Beschreibung: | 1 online resource |
| ISBN: | 9781400882557 |
| DOI: | 10.1515/9781400882557 |
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| 500 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) | ||
| 520 | |a Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps | ||
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Datensatz im Suchindex
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| author | McMullen, Curtis T. 1958- |
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| author_sort | McMullen, Curtis T. 1958- |
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| bvnumber | BV043712515 |
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| dewey-full | 530.1/43/0151 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/43/0151 |
| dewey-search | 530.1/43/0151 |
| dewey-sort | 3530.1 243 3151 |
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| discipline | Physik Mathematik |
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| id | DE-604.BV043712515 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:33:08Z |
| institution | BVB |
| isbn | 9781400882557 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029124743 |
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| physical | 1 online resource |
| psigel | ZDB-23-DGG ZDB-23-PST |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spelling | McMullen, Curtis T. 1958- (DE-588)172849853 aut Complex dynamics and renormalization Curtis T. McMullen Princeton, NJ Princeton University Press [1995] © 1995 1 online resource txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 135 Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps In English Mathematische Physik Dynamics Mathematical physics Polynomials Renormalization (Physics) Renormierung (DE-588)4128419-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Dynamik (DE-588)4013384-9 gnd rswk-swf Dynamik (DE-588)4013384-9 s Polynom (DE-588)4046711-9 s 1\p DE-604 Renormierung (DE-588)4128419-7 s Dynamisches System (DE-588)4013396-5 s 2\p DE-604 3\p DE-604 Erscheint auch als Druck-Ausgabe 978-0-691-02981-8 Annals of Mathematics Studies number 135 (DE-604)BV040389493 135 https://doi.org/10.1515/9781400882557?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | McMullen, Curtis T. 1958- Complex dynamics and renormalization Annals of Mathematics Studies Mathematische Physik Dynamics Mathematical physics Polynomials Renormalization (Physics) Renormierung (DE-588)4128419-7 gnd Dynamisches System (DE-588)4013396-5 gnd Polynom (DE-588)4046711-9 gnd Dynamik (DE-588)4013384-9 gnd |
| subject_GND | (DE-588)4128419-7 (DE-588)4013396-5 (DE-588)4046711-9 (DE-588)4013384-9 |
| title | Complex dynamics and renormalization |
| title_auth | Complex dynamics and renormalization |
| title_exact_search | Complex dynamics and renormalization |
| title_full | Complex dynamics and renormalization Curtis T. McMullen |
| title_fullStr | Complex dynamics and renormalization Curtis T. McMullen |
| title_full_unstemmed | Complex dynamics and renormalization Curtis T. McMullen |
| title_short | Complex dynamics and renormalization |
| title_sort | complex dynamics and renormalization |
| topic | Mathematische Physik Dynamics Mathematical physics Polynomials Renormalization (Physics) Renormierung (DE-588)4128419-7 gnd Dynamisches System (DE-588)4013396-5 gnd Polynom (DE-588)4046711-9 gnd Dynamik (DE-588)4013384-9 gnd |
| topic_facet | Mathematische Physik Dynamics Mathematical physics Polynomials Renormalization (Physics) Renormierung Dynamisches System Polynom Dynamik |
| url | https://doi.org/10.1515/9781400882557?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT mcmullencurtist complexdynamicsandrenormalization |