Chaos, dynamics, and fractals: an algorithmic approach to deterministic chaos
This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as w...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1993
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| Schriftenreihe: | Cambridge nonlinear science series
2 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xxi, 323 pages) |
| ISBN: | 9780511564154 |
| DOI: | 10.1017/CBO9780511564154 |
Internformat
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Datensatz im Suchindex
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| any_adam_object | |
| author | McCauley, Joseph L. |
| author_facet | McCauley, Joseph L. |
| author_role | aut |
| author_sort | McCauley, Joseph L. |
| author_variant | j l m jl jlm |
| building | Verbundindex |
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| dewey-full | 516.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.15 |
| dewey-search | 516.15 |
| dewey-sort | 3516.15 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1017/CBO9780511564154 |
| format | Electronic eBook |
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| id | DE-604.BV043942373 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511564154 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351343 |
| oclc_num | 992928166 |
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| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xxi, 323 pages) |
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| publishDate | 1993 |
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| publisher | Cambridge University Press |
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| spelling | McCauley, Joseph L. Verfasser aut Chaos, dynamics, and fractals an algorithmic approach to deterministic chaos Joseph L. McCauley Chaos, Dynamics, & Fractals Cambridge Cambridge University Press 1993 1 online resource (xxi, 323 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge nonlinear science series 2 Title from publisher's bibliographic system (viewed on 05 Oct 2015) This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed Mathematische Physik Deterministic chaos Algorithms Mappings (Mathematics) Fractals Mathematical physics Chaos (DE-588)4191419-3 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Fraktal (DE-588)4123220-3 s Chaostheorie (DE-588)4009754-7 s 1\p DE-604 Algorithmus (DE-588)4001183-5 s 2\p DE-604 Chaos (DE-588)4191419-3 s 3\p DE-604 Dynamisches System (DE-588)4013396-5 s 4\p DE-604 Erscheint auch als Druckausgabe 978-0-521-41658-0 Erscheint auch als Druckausgabe 978-0-521-46747-6 https://doi.org/10.1017/CBO9780511564154 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 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | McCauley, Joseph L. Chaos, dynamics, and fractals an algorithmic approach to deterministic chaos Mathematische Physik Deterministic chaos Algorithms Mappings (Mathematics) Fractals Mathematical physics Chaos (DE-588)4191419-3 gnd Dynamisches System (DE-588)4013396-5 gnd Fraktal (DE-588)4123220-3 gnd Chaostheorie (DE-588)4009754-7 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4191419-3 (DE-588)4013396-5 (DE-588)4123220-3 (DE-588)4009754-7 (DE-588)4001183-5 |
| title | Chaos, dynamics, and fractals an algorithmic approach to deterministic chaos |
| title_alt | Chaos, Dynamics, & Fractals |
| title_auth | Chaos, dynamics, and fractals an algorithmic approach to deterministic chaos |
| title_exact_search | Chaos, dynamics, and fractals an algorithmic approach to deterministic chaos |
| title_full | Chaos, dynamics, and fractals an algorithmic approach to deterministic chaos Joseph L. McCauley |
| title_fullStr | Chaos, dynamics, and fractals an algorithmic approach to deterministic chaos Joseph L. McCauley |
| title_full_unstemmed | Chaos, dynamics, and fractals an algorithmic approach to deterministic chaos Joseph L. McCauley |
| title_short | Chaos, dynamics, and fractals |
| title_sort | chaos dynamics and fractals an algorithmic approach to deterministic chaos |
| title_sub | an algorithmic approach to deterministic chaos |
| topic | Mathematische Physik Deterministic chaos Algorithms Mappings (Mathematics) Fractals Mathematical physics Chaos (DE-588)4191419-3 gnd Dynamisches System (DE-588)4013396-5 gnd Fraktal (DE-588)4123220-3 gnd Chaostheorie (DE-588)4009754-7 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Mathematische Physik Deterministic chaos Algorithms Mappings (Mathematics) Fractals Mathematical physics Chaos Dynamisches System Fraktal Chaostheorie Algorithmus |
| url | https://doi.org/10.1017/CBO9780511564154 |
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