Continuous and discontinuous piecewise-smooth one-dimensional maps: invariant sets and bifurcation structures
"The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invar...
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Publishing Company Pte Limited
2019
|
| Schriftenreihe: | World Scientific series on nonlinear science
v. 95 |
| Schlagworte: | |
| Online-Zugang: | UBY01 Volltext |
| Zusammenfassung: | "The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches."-- |
| Beschreibung: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader |
| Beschreibung: | 1 online resource (648 pages) illustrations |
| ISBN: | 9789814368834 |
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| 245 | 1 | 0 | |a Continuous and discontinuous piecewise-smooth one-dimensional maps |b invariant sets and bifurcation structures |c Viktor Avrutin ... [and others] |
| 264 | 1 | |a Singapore |b World Scientific Publishing Company Pte Limited |c 2019 | |
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| 490 | 0 | |a World Scientific series on nonlinear science |v v. 95 | |
| 500 | |a Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader | ||
| 505 | 8 | |a Includes bibliographical references and index | |
| 505 | 8 | |a General concepts and tools -- Bifurcations in piecewise smooth maps -- Bifurcation scenarios (overview) -- Map replacement -- Skew tent map -- Adding structures -- Incrementing structures -- Organizing centers | |
| 520 | |a "The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches."-- | ||
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Mappings (Mathematics) | |
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Datensatz im Suchindex
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| contents | Includes bibliographical references and index General concepts and tools -- Bifurcations in piecewise smooth maps -- Bifurcation scenarios (overview) -- Map replacement -- Skew tent map -- Adding structures -- Incrementing structures -- Organizing centers |
| ctrlnum | (ZDB-124-WOP)00008285 (OCoLC)1190675949 (DE-599)BVBBV046808862 |
| discipline | Wirtschaftswissenschaften |
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| id | DE-604.BV046808862 |
| illustrated | Illustrated |
| index_date | 2024-07-03T14:58:22Z |
| indexdate | 2024-07-10T08:54:26Z |
| institution | BVB |
| isbn | 9789814368834 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032217464 |
| oclc_num | 1190675949 |
| open_access_boolean | |
| owner | DE-706 |
| owner_facet | DE-706 |
| physical | 1 online resource (648 pages) illustrations |
| psigel | ZDB-124-WOP |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | World Scientific Publishing Company Pte Limited |
| record_format | marc |
| series2 | World Scientific series on nonlinear science |
| spelling | Continuous and discontinuous piecewise-smooth one-dimensional maps invariant sets and bifurcation structures Viktor Avrutin ... [and others] Singapore World Scientific Publishing Company Pte Limited 2019 1 online resource (648 pages) illustrations txt rdacontent c rdamedia cr rdacarrier World Scientific series on nonlinear science v. 95 Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references and index General concepts and tools -- Bifurcations in piecewise smooth maps -- Bifurcation scenarios (overview) -- Map replacement -- Skew tent map -- Adding structures -- Incrementing structures -- Organizing centers "The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches."-- Differentiable dynamical systems Mappings (Mathematics) Bifurcation theory Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Stückweise glatte Abbildung (DE-588)7601984-6 gnd rswk-swf Electronic books Stückweise glatte Abbildung (DE-588)7601984-6 s Verzweigung Mathematik (DE-588)4078889-1 s DE-604 Avrutin, Viktor Sonstige oth Erscheint auch als Druck-Ausgabe 9789814368827 https://www.worldscientific.com/worldscibooks/10.1142/8285 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Continuous and discontinuous piecewise-smooth one-dimensional maps invariant sets and bifurcation structures Includes bibliographical references and index General concepts and tools -- Bifurcations in piecewise smooth maps -- Bifurcation scenarios (overview) -- Map replacement -- Skew tent map -- Adding structures -- Incrementing structures -- Organizing centers Differentiable dynamical systems Mappings (Mathematics) Bifurcation theory Verzweigung Mathematik (DE-588)4078889-1 gnd Stückweise glatte Abbildung (DE-588)7601984-6 gnd |
| subject_GND | (DE-588)4078889-1 (DE-588)7601984-6 |
| title | Continuous and discontinuous piecewise-smooth one-dimensional maps invariant sets and bifurcation structures |
| title_auth | Continuous and discontinuous piecewise-smooth one-dimensional maps invariant sets and bifurcation structures |
| title_exact_search | Continuous and discontinuous piecewise-smooth one-dimensional maps invariant sets and bifurcation structures |
| title_exact_search_txtP | Continuous and discontinuous piecewise-smooth one-dimensional maps invariant sets and bifurcation structures |
| title_full | Continuous and discontinuous piecewise-smooth one-dimensional maps invariant sets and bifurcation structures Viktor Avrutin ... [and others] |
| title_fullStr | Continuous and discontinuous piecewise-smooth one-dimensional maps invariant sets and bifurcation structures Viktor Avrutin ... [and others] |
| title_full_unstemmed | Continuous and discontinuous piecewise-smooth one-dimensional maps invariant sets and bifurcation structures Viktor Avrutin ... [and others] |
| title_short | Continuous and discontinuous piecewise-smooth one-dimensional maps |
| title_sort | continuous and discontinuous piecewise smooth one dimensional maps invariant sets and bifurcation structures |
| title_sub | invariant sets and bifurcation structures |
| topic | Differentiable dynamical systems Mappings (Mathematics) Bifurcation theory Verzweigung Mathematik (DE-588)4078889-1 gnd Stückweise glatte Abbildung (DE-588)7601984-6 gnd |
| topic_facet | Differentiable dynamical systems Mappings (Mathematics) Bifurcation theory Verzweigung Mathematik Stückweise glatte Abbildung |
| url | https://www.worldscientific.com/worldscibooks/10.1142/8285 |
| work_keys_str_mv | AT avrutinviktor continuousanddiscontinuouspiecewisesmoothonedimensionalmapsinvariantsetsandbifurcationstructures |