Analytic Theory of Global Bifurcation:
Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are connected sets of solutions...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2016]
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| Schriftenreihe: | Princeton Series in Applied Mathematics
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are connected sets of solutions of global extent. Even when the operators are infinitely differentiable in all the variables and parameters, connectedness here cannot in general be replaced by path-connectedness. However, in the context of real-analyticity there is an alternative theory of global bifurcation due to Dancer, which offers a much stronger notion of parameter dependence. This book aims to develop from first principles Dancer's global bifurcation theory for one-parameter families of real-analytic operators in Banach spaces. It shows that there are globally defined continuous and locally real-analytic curves of solutions. In particular, in the real-analytic setting, local analysis can lead to global consequences--for example, as explained in detail here, those resulting from bifurcation from a simple eigenvalue. Included are accounts of analyticity and implicit function theorems in Banach spaces, classical results from the theory of finite-dimensional analytic varieties, and the links between these two and global existence theory. Laying the foundations for more extensive studies of real-analyticity in infinite-dimensional problems and illustrating the theory with examples, Analytic Theory of Global Bifurcation is intended for graduate students and researchers in pure and applied analysis |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Nov. 7, 2016) |
| Beschreibung: | 1 online resource |
| ISBN: | 9781400884339 |
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Datensatz im Suchindex
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| author | Buffoni, Boris 1965- |
| author_GND | (DE-588)1146433263 |
| author_facet | Buffoni, Boris 1965- |
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| author_sort | Buffoni, Boris 1965- |
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| dewey-full | 515/.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.35 |
| dewey-search | 515/.35 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043979338 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:40:14Z |
| institution | BVB |
| isbn | 9781400884339 |
| language | English |
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| publisher | Princeton University Press |
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| spelling | Buffoni, Boris 1965- Verfasser (DE-588)1146433263 aut Analytic Theory of Global Bifurcation Boris Buffoni, John Toland Princeton, NJ Princeton University Press [2016] © 2003 1 online resource txt rdacontent c rdamedia cr rdacarrier Princeton Series in Applied Mathematics Description based on online resource; title from PDF title page (publisher's Web site, viewed Nov. 7, 2016) Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are connected sets of solutions of global extent. Even when the operators are infinitely differentiable in all the variables and parameters, connectedness here cannot in general be replaced by path-connectedness. However, in the context of real-analyticity there is an alternative theory of global bifurcation due to Dancer, which offers a much stronger notion of parameter dependence. This book aims to develop from first principles Dancer's global bifurcation theory for one-parameter families of real-analytic operators in Banach spaces. It shows that there are globally defined continuous and locally real-analytic curves of solutions. In particular, in the real-analytic setting, local analysis can lead to global consequences--for example, as explained in detail here, those resulting from bifurcation from a simple eigenvalue. Included are accounts of analyticity and implicit function theorems in Banach spaces, classical results from the theory of finite-dimensional analytic varieties, and the links between these two and global existence theory. Laying the foundations for more extensive studies of real-analyticity in infinite-dimensional problems and illustrating the theory with examples, Analytic Theory of Global Bifurcation is intended for graduate students and researchers in pure and applied analysis In English Bifurcation theory Globale Verzweigung (DE-588)4374566-0 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Globale Verzweigung (DE-588)4374566-0 s Funktionalanalysis (DE-588)4018916-8 s 1\p DE-604 Toland, John Sonstige oth https://www.degruyter.com/doi/book/10.1515/9781400884339 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Buffoni, Boris 1965- Analytic Theory of Global Bifurcation Bifurcation theory Globale Verzweigung (DE-588)4374566-0 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4374566-0 (DE-588)4018916-8 |
| title | Analytic Theory of Global Bifurcation |
| title_auth | Analytic Theory of Global Bifurcation |
| title_exact_search | Analytic Theory of Global Bifurcation |
| title_full | Analytic Theory of Global Bifurcation Boris Buffoni, John Toland |
| title_fullStr | Analytic Theory of Global Bifurcation Boris Buffoni, John Toland |
| title_full_unstemmed | Analytic Theory of Global Bifurcation Boris Buffoni, John Toland |
| title_short | Analytic Theory of Global Bifurcation |
| title_sort | analytic theory of global bifurcation |
| topic | Bifurcation theory Globale Verzweigung (DE-588)4374566-0 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Bifurcation theory Globale Verzweigung Funktionalanalysis |
| url | https://www.degruyter.com/doi/book/10.1515/9781400884339 |
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