Canard cycles and center manifolds:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, RI
1996
|
| Schriftenreihe: | American Mathematical Society: Memoirs of the American Mathematical Society
577 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007205560&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Volume 121, Number 577 (first of 4 numbers) |
| Umfang: | IX, 100 S. graph. Darst. |
| ISBN: | 082180443X |
Internformat
MARC
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| 245 | 1 | 0 | |a Canard cycles and center manifolds |c Freddy Dumortier ; Robert Roussarie |
| 264 | 1 | |a Providence, RI |c 1996 | |
| 300 | |a IX, 100 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a American Mathematical Society: Memoirs of the American Mathematical Society |v 577 | |
| 500 | |a Volume 121, Number 577 (first of 4 numbers) | ||
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007205560 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 B 990-577/580 |
|---|---|
| DE-BY-TUM_katkey | 1565477 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020487756 |
| _version_ | 1821933965284474880 |
| adam_text | TABLE OF CONTENTS
1 Statement of the result : the canard phenomenon for the singular
Van der Pol equation 3
2 Global desingularization 10
2.1 Survey of the const ruction 10
2.2 Blow up at .s,, = 0 = (0,0,0,0) 13
2.2.1 Family Rescaling 15
2.2.2 Phase directional rescaling 17
2.2.3 Global pictures for X1 near ,s0 22
2.3 Blow up at no ( 1,1/6.0,0) 25
2.3.1 Family Rescaling 26
2.3.2 Phase directional charts 27
2.3.3 Global pictures for X2 near L2 U {.s0. ,} 30
2.4 Blowing up along N. S 32
2.5 Final blow up 34
3 Foliations by center manifolds 36
3.1 Normal forms for X at the non isolated singular points 3(j
3.2 Construction of center manifolds 41
3.2.1 Center manifolds of type I 42
3.2.2 Center manifolds of type II 46
3.2.3 Center manifolds of type III 50
3.2.4 Pictures of the center manifolds 51
3.3 Foliations by center manifolds 52
3.3.1 Foliation of type I 52
3.3.2 Foliation of type 11 66
3.3.3 Foliations of type III 71
vii
viii TABLE OF CONTENTS
4 The canard phenomenon 73
4.1 The small limit periodic set 73
4.2 Relation between the Abelian integrals and the center manifolds ... 77
4.3 Explanation of the canard phenomenon by means of center manifolds 81
4.3.1 Canard limit periodic sets of type I 81
4.3.2 Canard limit periodic sets of type III 88
4.3.3 Canard limit periodic sets of type II 89
4.3.4 Bringing the foliations together (as a final step) 91
References 95
Appendix : on the proof of theorem 18 (by Chengzhi Li) 97
|
| any_adam_object | 1 |
| author | Dumortier, Freddy 1947- Roussarie, Robert H. |
| author_GND | (DE-588)103726049X (DE-588)1124690379 |
| author_facet | Dumortier, Freddy 1947- Roussarie, Robert H. |
| author_role | aut aut |
| author_sort | Dumortier, Freddy 1947- |
| author_variant | f d fd r h r rh rhr |
| building | Verbundindex |
| bvnumber | BV010787093 |
| classification_rvk | SI 130 |
| ctrlnum | (OCoLC)243831292 (DE-599)BVBBV010787093 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010787093 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:00:42Z |
| institution | BVB |
| isbn | 082180443X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007205560 |
| oclc_num | 243831292 |
| open_access_boolean | |
| owner | DE-824 DE-355 DE-BY-UBR DE-12 DE-384 DE-739 DE-29T DE-91G DE-BY-TUM DE-83 DE-188 |
| owner_facet | DE-824 DE-355 DE-BY-UBR DE-12 DE-384 DE-739 DE-29T DE-91G DE-BY-TUM DE-83 DE-188 |
| physical | IX, 100 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| record_format | marc |
| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spellingShingle | Dumortier, Freddy 1947- Roussarie, Robert H. Canard cycles and center manifolds American Mathematical Society: Memoirs of the American Mathematical Society Störungstheorie (DE-588)4128420-3 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Asymptotische Methode (DE-588)4287476-2 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4128420-3 (DE-588)4078889-1 (DE-588)4287476-2 (DE-588)4048395-2 |
| title | Canard cycles and center manifolds |
| title_auth | Canard cycles and center manifolds |
| title_exact_search | Canard cycles and center manifolds |
| title_full | Canard cycles and center manifolds Freddy Dumortier ; Robert Roussarie |
| title_fullStr | Canard cycles and center manifolds Freddy Dumortier ; Robert Roussarie |
| title_full_unstemmed | Canard cycles and center manifolds Freddy Dumortier ; Robert Roussarie |
| title_short | Canard cycles and center manifolds |
| title_sort | canard cycles and center manifolds |
| topic | Störungstheorie (DE-588)4128420-3 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Asymptotische Methode (DE-588)4287476-2 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Störungstheorie Verzweigung Mathematik Asymptotische Methode Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007205560&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT dumortierfreddy canardcyclesandcentermanifolds AT roussarieroberth canardcyclesandcentermanifolds |
Inhaltsverzeichnis
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 001z 2001 B 990-577/580 Lageplan |
|---|---|
| Exemplar 1 |
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InhaltFolgende Werke befinden sich in dem Buch mit der oben genannten Signatur. |