Applications of Centre Manifold Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1982
|
| Schriftenreihe: | Applied Mathematical Sciences
35 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | These notes are based on a series of lectures given in the Lefschetz Center for Dynamical Systems in the Division of Applied Mathematics at Brown University during the academic year 1978-79. The purpose of the lectures was to give an introduction to the applications of centre manifold theory to differential equations. Most of the material is presented in an informal fashion, by means of worked examples in the hope that this clarifies the use of centre manifold theory. The main application of centre manifold theory given in these notes is to dynamic bifurcation theory. Dynamic bifurcation theory is concerned with topological changes in the nature of the solutions of differential equations as para meters are varied. Such an example is the creation of periodic orbits from an equilibrium point as a parameter crosses a critical value. In certain circumstances, the application of centre manifold theory reduces the dimension of the system under investigation. In this respect the centre manifold theory plays the same role for dynamic problems as the Liapunov-Schmitt procedure plays for the analysis of static solutions. Our use of centre manifold theory in bifurcation problems follows that of Ruelle and Takens [57) and of Marsden and McCracken [51) |
| Beschreibung: | 1 Online-Ressource (XII, 160p) |
| ISBN: | 9781461259299 9780387905778 |
| ISSN: | 0066-5452 |
| DOI: | 10.1007/978-1-4612-5929-9 |
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Datensatz im Suchindex
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| dewey-full | 514.34 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| dewey-search | 514.34 |
| dewey-sort | 3514.34 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-5929-9 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9781461259299 9780387905778 |
| issn | 0066-5452 |
| language | English |
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| spelling | Carr, Jack Verfasser aut Applications of Centre Manifold Theory by Jack Carr New York, NY Springer US 1982 1 Online-Ressource (XII, 160p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 35 0066-5452 These notes are based on a series of lectures given in the Lefschetz Center for Dynamical Systems in the Division of Applied Mathematics at Brown University during the academic year 1978-79. The purpose of the lectures was to give an introduction to the applications of centre manifold theory to differential equations. Most of the material is presented in an informal fashion, by means of worked examples in the hope that this clarifies the use of centre manifold theory. The main application of centre manifold theory given in these notes is to dynamic bifurcation theory. Dynamic bifurcation theory is concerned with topological changes in the nature of the solutions of differential equations as para meters are varied. Such an example is the creation of periodic orbits from an equilibrium point as a parameter crosses a critical value. In certain circumstances, the application of centre manifold theory reduces the dimension of the system under investigation. In this respect the centre manifold theory plays the same role for dynamic problems as the Liapunov-Schmitt procedure plays for the analysis of static solutions. Our use of centre manifold theory in bifurcation problems follows that of Ruelle and Takens [57) and of Marsden and McCracken [51) Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Verzweigung Mathematik (DE-588)4078889-1 s 1\p DE-604 Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s 2\p DE-604 https://doi.org/10.1007/978-1-4612-5929-9 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 | Carr, Jack Applications of Centre Manifold Theory Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Verzweigung Mathematik (DE-588)4078889-1 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd |
| subject_GND | (DE-588)4078889-1 (DE-588)4037379-4 (DE-588)4012269-4 |
| title | Applications of Centre Manifold Theory |
| title_auth | Applications of Centre Manifold Theory |
| title_exact_search | Applications of Centre Manifold Theory |
| title_full | Applications of Centre Manifold Theory by Jack Carr |
| title_fullStr | Applications of Centre Manifold Theory by Jack Carr |
| title_full_unstemmed | Applications of Centre Manifold Theory by Jack Carr |
| title_short | Applications of Centre Manifold Theory |
| title_sort | applications of centre manifold theory |
| topic | Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Verzweigung Mathematik (DE-588)4078889-1 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd |
| topic_facet | Mathematics Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Verzweigung Mathematik Mannigfaltigkeit Differenzierbare Mannigfaltigkeit |
| url | https://doi.org/10.1007/978-1-4612-5929-9 |
| work_keys_str_mv | AT carrjack applicationsofcentremanifoldtheory |