Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1983
|
| Schriftenreihe: | Applied Mathematical Sciences
42 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning 'strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #American Mathematical Monthly#2 |
| Beschreibung: | 1 Online-Ressource (XVI, 462 p) |
| ISBN: | 9781461211402 9781461270201 |
| ISSN: | 0066-5452 |
| DOI: | 10.1007/978-1-4612-1140-2 |
Internformat
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| 245 | 1 | 0 | |a Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields |c by John Guckenheimer, Philip Holmes |
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| 500 | |a From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning 'strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #American Mathematical Monthly#2 | ||
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Datensatz im Suchindex
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| author | Guckenheimer, John 1945- |
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| author_facet | Guckenheimer, John 1945- |
| author_role | aut |
| author_sort | Guckenheimer, John 1945- |
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| building | Verbundindex |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1140-2 |
| format | Electronic eBook |
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| id | DE-604.BV042419763 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461211402 9781461270201 |
| issn | 0066-5452 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855180 |
| oclc_num | 1184729923 |
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| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XVI, 462 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Applied Mathematical Sciences |
| spelling | Guckenheimer, John 1945- Verfasser (DE-588)172109353 aut Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by John Guckenheimer, Philip Holmes New York, NY Springer New York 1983 1 Online-Ressource (XVI, 462 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 42 0066-5452 From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning 'strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #American Mathematical Monthly#2 Mathematics Global analysis (Mathematics) Analysis Mathematik Dynamisches System (DE-588)4013396-5 gnd rswk-swf Nichtlineare Schwingung (DE-588)4042100-4 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Elektrische Schwingung (DE-588)4286651-0 gnd rswk-swf Nichtlineare Schwingung (DE-588)4042100-4 s Dynamisches System (DE-588)4013396-5 s Verzweigung Mathematik (DE-588)4078889-1 s 1\p DE-604 Differentialgleichung (DE-588)4012249-9 s 2\p DE-604 Elektrische Schwingung (DE-588)4286651-0 s 3\p DE-604 Holmes, Philip 1945- Sonstige (DE-588)1058917994 oth https://doi.org/10.1007/978-1-4612-1140-2 Verlag 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 | Guckenheimer, John 1945- Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields Mathematics Global analysis (Mathematics) Analysis Mathematik Dynamisches System (DE-588)4013396-5 gnd Nichtlineare Schwingung (DE-588)4042100-4 gnd Differentialgleichung (DE-588)4012249-9 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Elektrische Schwingung (DE-588)4286651-0 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4042100-4 (DE-588)4012249-9 (DE-588)4078889-1 (DE-588)4286651-0 |
| title | Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields |
| title_auth | Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields |
| title_exact_search | Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields |
| title_full | Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by John Guckenheimer, Philip Holmes |
| title_fullStr | Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by John Guckenheimer, Philip Holmes |
| title_full_unstemmed | Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by John Guckenheimer, Philip Holmes |
| title_short | Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields |
| title_sort | nonlinear oscillations dynamical systems and bifurcations of vector fields |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Dynamisches System (DE-588)4013396-5 gnd Nichtlineare Schwingung (DE-588)4042100-4 gnd Differentialgleichung (DE-588)4012249-9 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Elektrische Schwingung (DE-588)4286651-0 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Dynamisches System Nichtlineare Schwingung Differentialgleichung Verzweigung Mathematik Elektrische Schwingung |
| url | https://doi.org/10.1007/978-1-4612-1140-2 |
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