Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Springer Basel
1998
|
| Ausgabe: | 1998. Reprint 2013 of the 1998 edition |
| Schriftenreihe: | Modern Birkhäuser Classics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets. The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations. - - - The book as a whole is a well-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in recently developed methods. The book, reflecting the state of the art, can also be used for teaching special courses. (Mathematical Reviews) |
| Beschreibung: | 1 Online-Ressource (XVII, 204 p.) 51 illus |
| ISBN: | 9783034807180 9783034807173 |
| ISSN: | 2197-1803 |
| DOI: | 10.1007/978-3-0348-0718-0 |
Internformat
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-0718-0 |
| edition | 1998. Reprint 2013 of the 1998 edition |
| format | Electronic eBook |
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| id | DE-604.BV042421850 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9783034807180 9783034807173 |
| issn | 2197-1803 |
| language | English |
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| physical | 1 Online-Ressource (XVII, 204 p.) 51 illus |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1998 |
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| publisher | Springer Basel |
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| series2 | Modern Birkhäuser Classics |
| spelling | Roussarie, Robert Verfasser aut Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem by Robert Roussarie 1998. Reprint 2013 of the 1998 edition Basel Springer Basel 1998 1 Online-Ressource (XVII, 204 p.) 51 illus txt rdacontent c rdamedia cr rdacarrier Modern Birkhäuser Classics 2197-1803 In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets. The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations. - - - The book as a whole is a well-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in recently developed methods. The book, reflecting the state of the art, can also be used for teaching special courses. (Mathematical Reviews) Mathematics Global analysis (Mathematics) Differentiable dynamical systems Global analysis Differential equations, partial Analysis Global Analysis and Analysis on Manifolds Partial Differential Equations Dynamical Systems and Ergodic Theory Mathematik Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Planares Vektorfeld (DE-588)4261750-9 gnd rswk-swf Hilbertsches Problem 16 (DE-588)4391597-8 gnd rswk-swf Planares Vektorfeld (DE-588)4261750-9 s Verzweigung Mathematik (DE-588)4078889-1 s 1\p DE-604 Hilbertsches Problem 16 (DE-588)4391597-8 s 2\p DE-604 https://doi.org/10.1007/978-3-0348-0718-0 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 |
| spellingShingle | Roussarie, Robert Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem Mathematics Global analysis (Mathematics) Differentiable dynamical systems Global analysis Differential equations, partial Analysis Global Analysis and Analysis on Manifolds Partial Differential Equations Dynamical Systems and Ergodic Theory Mathematik Verzweigung Mathematik (DE-588)4078889-1 gnd Planares Vektorfeld (DE-588)4261750-9 gnd Hilbertsches Problem 16 (DE-588)4391597-8 gnd |
| subject_GND | (DE-588)4078889-1 (DE-588)4261750-9 (DE-588)4391597-8 |
| title | Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem |
| title_auth | Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem |
| title_exact_search | Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem |
| title_full | Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem by Robert Roussarie |
| title_fullStr | Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem by Robert Roussarie |
| title_full_unstemmed | Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem by Robert Roussarie |
| title_short | Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem |
| title_sort | bifurcations of planar vector fields and hilbert s sixteenth problem |
| topic | Mathematics Global analysis (Mathematics) Differentiable dynamical systems Global analysis Differential equations, partial Analysis Global Analysis and Analysis on Manifolds Partial Differential Equations Dynamical Systems and Ergodic Theory Mathematik Verzweigung Mathematik (DE-588)4078889-1 gnd Planares Vektorfeld (DE-588)4261750-9 gnd Hilbertsches Problem 16 (DE-588)4391597-8 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Differentiable dynamical systems Global analysis Differential equations, partial Analysis Global Analysis and Analysis on Manifolds Partial Differential Equations Dynamical Systems and Ergodic Theory Mathematik Verzweigung Mathematik Planares Vektorfeld Hilbertsches Problem 16 |
| url | https://doi.org/10.1007/978-3-0348-0718-0 |
| work_keys_str_mv | AT roussarierobert bifurcationsofplanarvectorfieldsandhilbertssixteenthproblem |