Fundamentals of dynamical systems and bifurcation theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Czech |
| Veröffentlicht: |
Bristol [u.a.]
Hilger
1992
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Tschech. übers. |
| Beschreibung: | VIII, 293 S. graph. Darst. |
| ISBN: | 0750301503 |
Internformat
MARC
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| 100 | 1 | |a Medved', Milan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fundamentals of dynamical systems and bifurcation theory |c Milan Medved' |
| 264 | 1 | |a Bristol [u.a.] |b Hilger |c 1992 | |
| 300 | |a VIII, 293 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Aus dem Tschech. übers. | ||
| 650 | 4 | |a Bifurcation, Théorie de la | |
| 650 | 4 | |a Dynamique différentiable | |
| 650 | 4 | |a Bifurcation theory | |
| 650 | 4 | |a Differentiable dynamical systems | |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
INTRODUCTION vii
1 SELECTED READING ON THE FOUNDATIONS OF ALGEBRA,
TOPOLOGY, MATHEMATICAL ANALYSIS AND THE THEORY
OF DIFFERENTIAL EQUATIONS 1
1.1 Some basic concepts and notation 1
1.2 Relations on a set 2
1.3 Linear, Euclidean and linear normed spaces 3
1.4 Metric spaces 5
1.5 Topological spaces 5
1.6 Matrices 9
1.7 Linear mappings 10
1.8 Mathematical analysis 12
1.9 Differential equations 18
2 FOUNDATIONS OF THE THEORY OF DIFFERENTIABLE
MANIFOLDS AND DIFFERENTIABLE MAPPINGS 22
2.1 C manifolds 22
2.2 Cr mappings 26
2.3 Tangent space to a Cr manifold 27
2.4 C submanifolds 32
2.5 C manifolds in RN 35
2.6 Immersion and submersion theorems 36
2.7 Regular and critical values of mappings 39
2.8 Topology on the space of Cr mappings 41
2.9 Jets 45
2.10 Transversality 46
2.11 Stratification of algebraic and semi algebraic manifolds 55
2.12 Transversality to stratification 61
3 VECTOR FIELDS AND DYNAMICAL SYSTEMS 63
3.1 Vector fields on differentiate manifolds 63
v
3.2 Limit properties of dynamical systems 75
3.3 Examples of vector fields 84
3.4 Generic properties of parameter dependent matrices 86
3.5 Linear dynamical systems and some notions from the theory
of non linear dynamical systems 103
3.6 Grobman Hartman Theorem 128
3.7 Normal forms of differential equations 143
3.8 Poincare mapping 159
4 INVARIANT MANIFOLDS 172
4.1 Stable and unstable manifolds 172
4.2 Centre manifolds 183
5 GENERIC BIFURCATIONS OF VECTOR FIELDS AND
DIFFEOMORPHISMS 203
5.1 Ljapunov Schmidt Method 203
5.2 Generic bifurcations of 1 parameter systems of vector fields
in neighbourhoods of singular points 214
5.3 Generic bifurcations of 1 parameter systems of diffeomorphisms 238
5.4 Generic bifurcations of 1 parameter systems of vector fields
in neighbourhoods of periodic trajectories 258
6 COMPLEMENTARY NOTES ON THE CONTEMPORARY
THEORY OF DYNAMICAL SYSTEMS 262
6.1 Generic bifurcations of multi parameter systems of
vector fields 262
6.2 Global theory of dynamical systems 270
6.3 Sifiiikov bifurcation 273
6.4 Global Hopf bifurcation 276
6.5 Attractors and chaotic sets 279
REFERENCES 282
SUBJECT INDEX 289
vi
|
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| id | DE-604.BV006618306 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:49:20Z |
| institution | BVB |
| isbn | 0750301503 |
| language | English Czech |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004229160 |
| oclc_num | 23973149 |
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| owner_facet | DE-91G DE-BY-TUM DE-739 DE-384 DE-29T DE-11 DE-188 |
| physical | VIII, 293 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Hilger |
| record_format | marc |
| spelling | Medved', Milan Verfasser aut Fundamentals of dynamical systems and bifurcation theory Milan Medved' Bristol [u.a.] Hilger 1992 VIII, 293 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus dem Tschech. übers. Bifurcation, Théorie de la Dynamique différentiable Bifurcation theory Differentiable dynamical systems Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Verzweigung Mathematik (DE-588)4078889-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004229160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Medved', Milan Fundamentals of dynamical systems and bifurcation theory Bifurcation, Théorie de la Dynamique différentiable Bifurcation theory Differentiable dynamical systems Verzweigung Mathematik (DE-588)4078889-1 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4078889-1 (DE-588)4137931-7 |
| title | Fundamentals of dynamical systems and bifurcation theory |
| title_auth | Fundamentals of dynamical systems and bifurcation theory |
| title_exact_search | Fundamentals of dynamical systems and bifurcation theory |
| title_full | Fundamentals of dynamical systems and bifurcation theory Milan Medved' |
| title_fullStr | Fundamentals of dynamical systems and bifurcation theory Milan Medved' |
| title_full_unstemmed | Fundamentals of dynamical systems and bifurcation theory Milan Medved' |
| title_short | Fundamentals of dynamical systems and bifurcation theory |
| title_sort | fundamentals of dynamical systems and bifurcation theory |
| topic | Bifurcation, Théorie de la Dynamique différentiable Bifurcation theory Differentiable dynamical systems Verzweigung Mathematik (DE-588)4078889-1 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Bifurcation, Théorie de la Dynamique différentiable Bifurcation theory Differentiable dynamical systems Verzweigung Mathematik Differenzierbares dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004229160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT medvedmilan fundamentalsofdynamicalsystemsandbifurcationtheory |