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Bibliographic Details
Main Authors:	Dumortier, Freddy 1947- (Author), Roussarie, Robert H. (Author)
Format:	Book
Language:	English
Published:	Providence, RI 1996
Series:	American Mathematical Society: Memoirs of the American Mathematical Society 577
Subjects:	Störungstheorie Verzweigung > Mathematik Asymptotische Methode Randwertproblem
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
Item Description:	Volume 121, Number 577 (first of 4 numbers)
Physical Description:	IX, 100 S. graph. Darst.
ISBN:	082180443X

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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.
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isbn	082180443X
language	English
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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

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Call Number:	0102 MAT 001z 2001 B 990-577/580 Floor plan
Copy 1	Available for loan On Shelf Contents The following works are all found in the book indicated by the call number above. Canard cycles and center manifolds Global aspects of homoclinic bifurcations of vector fields Lebesgue theory in the bidual of C(X) Reductive subgroups of exceptional algebraic groups