Differential Equations and Dynamical Systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1991
|
| Schriftenreihe: | Texts in Applied Mathematics
7 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition contains materials on higher order Melnikov functions and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems |
| Beschreibung: | 1 Online-Ressource (XII, 407p. 177 illus) |
| ISBN: | 9781468403923 9781468403947 |
| ISSN: | 0939-2475 |
| DOI: | 10.1007/978-1-4684-0392-3 |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Perko, Lawrence |
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| author_sort | Perko, Lawrence |
| author_variant | l p lp |
| building | Verbundindex |
| bvnumber | BV042421039 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-0392-3 |
| format | Electronic eBook |
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| id | DE-604.BV042421039 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468403923 9781468403947 |
| issn | 0939-2475 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856456 |
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| physical | 1 Online-Ressource (XII, 407p. 177 illus) |
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| spelling | Perko, Lawrence Verfasser aut Differential Equations and Dynamical Systems by Lawrence Perko New York, NY Springer US 1991 1 Online-Ressource (XII, 407p. 177 illus) txt rdacontent c rdamedia cr rdacarrier Texts in Applied Mathematics 7 0939-2475 This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition contains materials on higher order Melnikov functions and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems Mathematics Global analysis (Mathematics) Analysis Mathematik Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Nichtlineare Differentialgleichung (DE-588)4205536-2 s 2\p DE-604 Dynamisches System (DE-588)4013396-5 s 3\p DE-604 Differentialgleichung (DE-588)4012249-9 s 4\p DE-604 System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 s 5\p DE-604 https://doi.org/10.1007/978-1-4684-0392-3 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 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Perko, Lawrence Differential Equations and Dynamical Systems Mathematics Global analysis (Mathematics) Analysis Mathematik Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Dynamisches System (DE-588)4013396-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4116671-1 (DE-588)4013396-5 (DE-588)4012249-9 (DE-588)4205536-2 (DE-588)4143389-0 |
| title | Differential Equations and Dynamical Systems |
| title_auth | Differential Equations and Dynamical Systems |
| title_exact_search | Differential Equations and Dynamical Systems |
| title_full | Differential Equations and Dynamical Systems by Lawrence Perko |
| title_fullStr | Differential Equations and Dynamical Systems by Lawrence Perko |
| title_full_unstemmed | Differential Equations and Dynamical Systems by Lawrence Perko |
| title_short | Differential Equations and Dynamical Systems |
| title_sort | differential equations and dynamical systems |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Dynamisches System (DE-588)4013396-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Gewöhnliche Differentialgleichung System von gewöhnlichen Differentialgleichungen Dynamisches System Differentialgleichung Nichtlineare Differentialgleichung Aufgabensammlung |
| url | https://doi.org/10.1007/978-1-4684-0392-3 |
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