Canard cycles and center manifolds:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
1996
|
| Series: | American Mathematical Society: Memoirs of the American Mathematical Society
577 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 121, Number 577 (first of 4 numbers) |
| Physical Description: | IX, 100 S. graph. Darst. |
| ISBN: | 082180443X |
Staff View
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. | ||
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Record in the Search Index
| _version_ | 1804125270159917056 |
|---|---|
| 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 | 2024-07-09T17:58:53Z |
| institution | BVB |
| isbn | 082180443X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007205560 |
| oclc_num | 243831292 |
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| physical | IX, 100 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
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| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Dumortier, Freddy 1947- Verfasser (DE-588)103726049X aut Canard cycles and center manifolds Freddy Dumortier ; Robert Roussarie Providence, RI 1996 IX, 100 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 577 Volume 121, Number 577 (first of 4 numbers) Störungstheorie (DE-588)4128420-3 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s Asymptotische Methode (DE-588)4287476-2 s DE-604 Verzweigung Mathematik (DE-588)4078889-1 s Störungstheorie (DE-588)4128420-3 s Roussarie, Robert H. Verfasser (DE-588)1124690379 aut American Mathematical Society: Memoirs of the American Mathematical Society 577 (DE-604)BV008000141 577 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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 |