Smooth invariant manifolds and normal forms:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore u.a.
World Scientific
1994
|
| Schriftenreihe: | [World scientific series on nonlinear science / A]
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 384 S. |
| ISBN: | 981021572X |
Internformat
MARC
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|---|---|---|---|
| 001 | BV010305085 | ||
| 003 | DE-604 | ||
| 005 | 19960119 | ||
| 007 | t | ||
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| 020 | |a 981021572X |9 981-02-1572-X | ||
| 035 | |a (OCoLC)32336249 | ||
| 035 | |a (DE-599)BVBBV010305085 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
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| 100 | 1 | |a Bronštejn, Ilʹja N. |d 1903-1976 |e Verfasser |0 (DE-588)104989742 |4 aut | |
| 245 | 1 | 0 | |a Smooth invariant manifolds and normal forms |c I. U. Bronstein and A. Ya. Kopanskii |
| 264 | 1 | |a Singapore u.a. |b World Scientific |c 1994 | |
| 300 | |a XII, 384 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a [World scientific series on nonlinear science / A] |v 7 | |
| 650 | 7 | |a Differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Dynamique différentiable |2 ram | |
| 650 | 7 | |a Dynamische systemen |2 gtt | |
| 650 | 7 | |a Formes normales (mathématiques) |2 ram | |
| 650 | 7 | |a Invariants |2 ram | |
| 650 | 7 | |a Manifolds |2 gtt | |
| 650 | 7 | |a Systèmes dynamiques |2 ram | |
| 650 | 7 | |a Variétés (mathématiques) |2 ram | |
| 650 | 4 | |a Bifurcation theory | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Invariant manifolds | |
| 650 | 4 | |a Normal forms (Mathematics) | |
| 650 | 0 | 7 | |a Glatte Mannigfaltigkeit |0 (DE-588)4157471-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Normalform |0 (DE-588)4172025-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Invarianz |0 (DE-588)4120518-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Glatte Mannigfaltigkeit |0 (DE-588)4157471-0 |D s |
| 689 | 0 | 1 | |a Invarianz |0 (DE-588)4120518-2 |D s |
| 689 | 0 | 2 | |a Normalform |0 (DE-588)4172025-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Kopanskij, A. J. |e Verfasser |4 aut | |
| 810 | 2 | |a A] |t [World scientific series on nonlinear science |v 7 |w (DE-604)BV009051753 |9 7 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006857055&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006857055 | ||
Datensatz im Suchindex
| _version_ | 1804124723988135936 |
|---|---|
| adam_text | V
CONTENTS
Introduction vii
Chapter I. Topological properties of flows and cascades in the vicinity
of a rest point and a periodic trajectory
§ 1. Basic definitions and facts 1
§ 2. Hyperbolic rest points 8
§ 3. Floquet Lyapunov theory 13
§ 4. Hadamard Bohl Perron theory 21
Chapter II. Finitely smooth normal forms of vector fields and diffeomorphisms
§ 1. The problem on reducing a C*° vector field to C* normal
form in the vicinity of a hyperbolic rest point 29
§ 2. Normalization of jets of vector fields and diffeomorphisms 34
§ 3. Polynomial normal forms 47
§ 4. Simplification of the resonant normal form via finitely
smooth transformations 67
§ 5. A general condition for C* linearizability 76
§ 6. C* linearization theorems 89
§ 7. Some sufücient conditions for C* linearizability 108
§ 8. Theorems on C* normal forms 136
§ 9. Linearization of finitely smooth vector fields
and diffeomorphisms 143
§ 10. Normal forms (a Supplement to § 8) 178
§ 11. Summary of results on finitely smooth normal forms 182
vi
Chapter in. Linear extensions of dynamkal Systems
§ 1. Basic notions and facts 193
§ 2. Exponential Separation and exponential Splitting 200
§ 3. The structure of linear extensions 206
§ 4. Quadratic Lyapunov functions 224
§ 5. Weak regularity and Green Samoilenko functions 230
§ 6. Smooth linear extensions 251
Chapter IV. Invariant subbundles of weakly non linear extensions
§ 1. Invariant subbundles and their intrinsic characterization 261
§ 2. The decomposition theorem 268
§ 3. The Grobman Hartman theorem 274
§ 4. Smooth invariant subbundles 278
Chapter V. Invariant manifolds
§ 1. Persistence of invariant manifolds 290
§ 2. Normal hyperbolicity and persistence 293
§ 3. Necessary condition for persistence 300
§ 4. Asymptotic phase 304
Chapter VI. Normal forms in the vicinity of an invariant manifold
§ 1. Polynomial normal forms (the nodal case) 318
§ 2. Polynomial normal forms (the saddle case) 332
Appendix. Some facts from global analysis 343
Bibliography 364
Subject index 380
List of symbols 384
|
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| author | Bronštejn, Ilʹja N. 1903-1976 Kopanskij, A. J. |
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| dewey-ones | 514 - Topology |
| dewey-raw | 514/.74 |
| dewey-search | 514/.74 |
| dewey-sort | 3514 274 |
| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV010305085 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:50:12Z |
| institution | BVB |
| isbn | 981021572X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006857055 |
| oclc_num | 32336249 |
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| owner_facet | DE-384 DE-11 DE-188 |
| physical | XII, 384 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | World Scientific |
| record_format | marc |
| series2 | [World scientific series on nonlinear science / A] |
| spelling | Bronštejn, Ilʹja N. 1903-1976 Verfasser (DE-588)104989742 aut Smooth invariant manifolds and normal forms I. U. Bronstein and A. Ya. Kopanskii Singapore u.a. World Scientific 1994 XII, 384 S. txt rdacontent n rdamedia nc rdacarrier [World scientific series on nonlinear science / A] 7 Differentiaalvergelijkingen gtt Dynamique différentiable ram Dynamische systemen gtt Formes normales (mathématiques) ram Invariants ram Manifolds gtt Systèmes dynamiques ram Variétés (mathématiques) ram Bifurcation theory Differentiable dynamical systems Invariant manifolds Normal forms (Mathematics) Glatte Mannigfaltigkeit (DE-588)4157471-0 gnd rswk-swf Normalform (DE-588)4172025-8 gnd rswk-swf Invarianz (DE-588)4120518-2 gnd rswk-swf Glatte Mannigfaltigkeit (DE-588)4157471-0 s Invarianz (DE-588)4120518-2 s Normalform (DE-588)4172025-8 s DE-604 Kopanskij, A. J. Verfasser aut A] [World scientific series on nonlinear science 7 (DE-604)BV009051753 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006857055&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bronštejn, Ilʹja N. 1903-1976 Kopanskij, A. J. Smooth invariant manifolds and normal forms Differentiaalvergelijkingen gtt Dynamique différentiable ram Dynamische systemen gtt Formes normales (mathématiques) ram Invariants ram Manifolds gtt Systèmes dynamiques ram Variétés (mathématiques) ram Bifurcation theory Differentiable dynamical systems Invariant manifolds Normal forms (Mathematics) Glatte Mannigfaltigkeit (DE-588)4157471-0 gnd Normalform (DE-588)4172025-8 gnd Invarianz (DE-588)4120518-2 gnd |
| subject_GND | (DE-588)4157471-0 (DE-588)4172025-8 (DE-588)4120518-2 |
| title | Smooth invariant manifolds and normal forms |
| title_auth | Smooth invariant manifolds and normal forms |
| title_exact_search | Smooth invariant manifolds and normal forms |
| title_full | Smooth invariant manifolds and normal forms I. U. Bronstein and A. Ya. Kopanskii |
| title_fullStr | Smooth invariant manifolds and normal forms I. U. Bronstein and A. Ya. Kopanskii |
| title_full_unstemmed | Smooth invariant manifolds and normal forms I. U. Bronstein and A. Ya. Kopanskii |
| title_short | Smooth invariant manifolds and normal forms |
| title_sort | smooth invariant manifolds and normal forms |
| topic | Differentiaalvergelijkingen gtt Dynamique différentiable ram Dynamische systemen gtt Formes normales (mathématiques) ram Invariants ram Manifolds gtt Systèmes dynamiques ram Variétés (mathématiques) ram Bifurcation theory Differentiable dynamical systems Invariant manifolds Normal forms (Mathematics) Glatte Mannigfaltigkeit (DE-588)4157471-0 gnd Normalform (DE-588)4172025-8 gnd Invarianz (DE-588)4120518-2 gnd |
| topic_facet | Differentiaalvergelijkingen Dynamique différentiable Dynamische systemen Formes normales (mathématiques) Invariants Manifolds Systèmes dynamiques Variétés (mathématiques) Bifurcation theory Differentiable dynamical systems Invariant manifolds Normal forms (Mathematics) Glatte Mannigfaltigkeit Normalform Invarianz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006857055&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009051753 |
| work_keys_str_mv | AT bronstejnilʹjan smoothinvariantmanifoldsandnormalforms AT kopanskijaj smoothinvariantmanifoldsandnormalforms |