Dynamical systems on surfaces:
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English French |
| Published: |
Berlin, [u.a.]
Springer
1983
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| Series: | Universitext
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 201 Seiten |
| ISBN: | 3540116451 0387116451 |
Staff View
MARC
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| 100 | 1 | |a Godbillon, Claude |d 1937-1990 |0 (DE-588)1103029630 |4 aut | |
| 240 | 1 | 0 | |a Systèmes dynamiques sur les surfaces |
| 245 | 1 | 0 | |a Dynamical systems on surfaces |c C. Godbillon ; translation from the French by H. G. Helfenstein |
| 264 | 1 | |a Berlin, [u.a.] |b Springer |c 1983 | |
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| 650 | 7 | |a Oppervlakken |2 gtt | |
| 650 | 7 | |a Systèmes dynamiques différentiables |2 ram | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Foliations (Mathematics) | |
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Record in the Search Index
| _version_ | 1821319979969019904 |
|---|---|
| adam_text |
Table of Contents
I. VECTOR FIELDS ON MANIFOLDS 1
1. Integration of vector fields. 1
2. General theory of orbits. 13
3. Invariant and minimal sets. 18
4. Limit sets. 21
5. Direction fields. 27
A. Vector fields and isotopies. 34
II. THE LOCAL BEHAVIOUR OF VECTOR FIELDS 39
1. Stability and conjugation. 39
2. Linear differential equations. 44
3. Linear differential equations with constant coefficients. 47
4. Linear differential equations with periodic coefficients. 50
5. Variation field of a vector field. 52
6. Behaviour near a singular point. 57
7. Behaviour near a periodic orbit. 59
A. Conjugation of contractions in R. 67
III. PLANAR VECTOR FIELDS 75
1. Limit sets in the plane. 75
2. Periodic orbits. 82
3. Singular points. 90
4. The Poincare index. 105
5. Planar direction fields. 116
6. Direction, fields on cylinders and Moebius strips. 123
A. Singular generic foliations of a disc. 127
IV. DIRECTION FIELDS ON THE TORUS AND HOMEOMORPHISMS OF THE CIRCLE 130
1. Direction fields on the torus. 130
2. Direction fields on a Klein bottle. 137
3. Homeomorphisms of the circle without periodic point. 144
4. Rotation number of Poincare. 151
5. Conjugation of circle homeomorphisms to rotations. 159
A. Homeomorphism groups of an interval. 166
B. Homeomorphism groups of the circle. 170
V. VECTOR FIELDS ON SURFACES 178
1. Classification of compact surfaces. 178
2. Vector fields on surfaces. 181
3. The index theorem. 188
A. Elements of differential geometry of surfaces. 191
BIBLIOGRAPHY 200 |
| any_adam_object | 1 |
| author | Godbillon, Claude 1937-1990 |
| author2 | Helfenstein, H. G. |
| author2_role | trl |
| author2_variant | h g h hg hgh |
| author_GND | (DE-588)1103029630 |
| author_facet | Godbillon, Claude 1937-1990 Helfenstein, H. G. |
| author_role | aut |
| author_sort | Godbillon, Claude 1937-1990 |
| author_variant | c g cg |
| building | Verbundindex |
| bvnumber | BV002285222 |
| callnumber-first | Q - Science |
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| classification_tum | MAT 344f |
| ctrlnum | (OCoLC)8866589 (DE-599)BVBBV002285222 |
| dewey-full | 516/.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.36 |
| dewey-search | 516/.36 |
| dewey-sort | 3516 236 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002285222 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-15T13:01:26Z |
| institution | BVB |
| isbn | 3540116451 0387116451 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001501883 |
| oclc_num | 8866589 |
| open_access_boolean | |
| owner | DE-384 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-188 |
| owner_facet | DE-384 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-188 |
| physical | 201 Seiten |
| psigel | TUB-nb |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Godbillon, Claude 1937-1990 (DE-588)1103029630 aut Systèmes dynamiques sur les surfaces Dynamical systems on surfaces C. Godbillon ; translation from the French by H. G. Helfenstein Berlin, [u.a.] Springer 1983 201 Seiten txt rdacontent n rdamedia nc rdacarrier Universitext Dynamique différentiable Dynamische systemen gtt Feuilletages (Mathématiques) Feuilletages (Mathématiques) ram Oppervlakken gtt Systèmes dynamiques différentiables ram Differentiable dynamical systems Foliations (Mathematics) Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Blätterung (DE-588)4007006-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Blätterung (DE-588)4007006-2 s DE-604 Mannigfaltigkeit (DE-588)4037379-4 s Helfenstein, H. G. trl Erscheint auch als Online-Ausgabe 978-3-642-68626-9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001501883&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Godbillon, Claude 1937-1990 Dynamical systems on surfaces Dynamique différentiable Dynamische systemen gtt Feuilletages (Mathématiques) Feuilletages (Mathématiques) ram Oppervlakken gtt Systèmes dynamiques différentiables ram Differentiable dynamical systems Foliations (Mathematics) Mannigfaltigkeit (DE-588)4037379-4 gnd Blätterung (DE-588)4007006-2 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4007006-2 (DE-588)4013396-5 |
| title | Dynamical systems on surfaces |
| title_alt | Systèmes dynamiques sur les surfaces |
| title_auth | Dynamical systems on surfaces |
| title_exact_search | Dynamical systems on surfaces |
| title_full | Dynamical systems on surfaces C. Godbillon ; translation from the French by H. G. Helfenstein |
| title_fullStr | Dynamical systems on surfaces C. Godbillon ; translation from the French by H. G. Helfenstein |
| title_full_unstemmed | Dynamical systems on surfaces C. Godbillon ; translation from the French by H. G. Helfenstein |
| title_short | Dynamical systems on surfaces |
| title_sort | dynamical systems on surfaces |
| topic | Dynamique différentiable Dynamische systemen gtt Feuilletages (Mathématiques) Feuilletages (Mathématiques) ram Oppervlakken gtt Systèmes dynamiques différentiables ram Differentiable dynamical systems Foliations (Mathematics) Mannigfaltigkeit (DE-588)4037379-4 gnd Blätterung (DE-588)4007006-2 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Dynamique différentiable Dynamische systemen Feuilletages (Mathématiques) Oppervlakken Systèmes dynamiques différentiables Differentiable dynamical systems Foliations (Mathematics) Mannigfaltigkeit Blätterung Dynamisches System |
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