Composite asymptotic expansions:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Schriftenreihe: | Lecture Notes in Mathematics
2066 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | X, 161 S. graph. Darst. |
| ISBN: | 3642340342 9783642340345 |
Internformat
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| 245 | 1 | 0 | |a Composite asymptotic expansions |c Augustin Fruchard ; Reinhard Schäfke |
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Datensatz im Suchindex
| _version_ | 1807954797916061696 |
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| adam_text |
IMAGE 1
CONTENTS
1 FOUR INTRODUCTORY EXAMPLES 1
1.1 FIRST EXAMPLE 1
1.2 EXTENSIONS 6
1.3 SECOND EXAMPLE 9
1.4 THIRD EXAMPLE 11
1.5 FOURTH EXAMPLE 13
1.6 COMPOSITE EXPANSIONS 14
2 COMPOSITE ASYMPTOTIC EXPANSIONS: GENERAL STUDY 17
2.1 NOTATION 17
2.2 COMPOSITE FORMAL SERIES 19
2.3 COMPOSITE EXPANSIONS: DEFINITION AND BASIC PROPERTIES 22
2.4 COMPOSITE EXPANSIONS AND MATCHING 29
2.5 CONTINUATION O F COMPOSITE EXPANSIONS 34
2.6 QUOTIENTS OF CASES 37
2.7 MULTIPLE CASES 4 0
3 COMPOSITE ASYMPTOTIC EXPANSIONS: GEVREY THEORY 43
3.1 COMPOSITE GEVREY FORMAL SERIES 43
3.2 COMPOSITE GEVREY ASYMPTOTIC EXPANSIONS 47
3.3 FLAT GEVREY FUNCTIONS 53
3.4 THEOREMS O F BOREL-RITT TYPE 55
3.5 CONSISTENT GOOD COVERINGS 59
4 A THEOREM O F RAMIS-SIBUYA TYPE 63
4.1 STATEMENT OF THE THEOREM AND BEGINNING OF THE PROOF 63
4.2 THE SLOW PART 67
4.3 THEFASTPART 7 0
4.4 STUDY OF THE FUNCTIONS GI 71
4.5 THE CASE ^ NEGATIVE 74
4.6 COMPOSITION O F A GEVREY CASE AND AN ANALYTIC FUNCTION 7 6
I X
HTTP://D-NB.INFO/1025944380
IMAGE 2
X C O N T E N T S
5 COMPOSITE EXPANSIONS AND SINGULARLY PERTURBED
DIFFERENTIAL EQUATIONS 81
5.1 CLASSICAL CASES AT A REGULAR POINT 82
5.2 CASES AT A TURNING POINT: THE QUASI-LINEAR CASE 89
5.2.1 COMPOSITE FORMAL SOLUTIONS 9 0
5.2.2 ANALYTIC SOLUTIONS AND CASES 9 3
5.2.3 THE GEVREY CHARACTER O F CASES 9 9
5.2.4 REMARKS AND EXTENSIONS 103
5.3 CASE AT A TURNING POINT: A GENERALIZATION 106
6 APPLICATIONS 119
6.1 CANARDS IN A MULTIPLE TURNING POINT 120
6.2 NON-SMOOTH CANARDS 126
6.2.1 EQUATIONS O F "UNION JACK" TYPE 126
6.2.2 NON-SMOOTH EQUATIONS 132
6.3 ACKERBERG-O'MALLEY RESONANCE 136
7 HISTORICAL REMARKS 151
REFERENCES 155
INDEX 159 |
| any_adam_object | 1 |
| author | Fruchard, Augustin Schäfke, Reinhard |
| author_GND | (DE-588)1030057753 (DE-588)1030059276 |
| author_facet | Fruchard, Augustin Schäfke, Reinhard |
| author_role | aut aut |
| author_sort | Fruchard, Augustin |
| author_variant | a f af r s rs |
| building | Verbundindex |
| bvnumber | BV040671010 |
| classification_rvk | SI 850 |
| classification_tum | MAT 346f |
| ctrlnum | (OCoLC)829219384 (DE-599)DNB1025944380 |
| dewey-full | 511.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.4 |
| dewey-search | 511.4 |
| dewey-sort | 3511.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-08-21T00:27:35Z |
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| isbn | 3642340342 9783642340345 |
| language | English |
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| physical | X, 161 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series | Lecture Notes in Mathematics |
| series2 | Lecture Notes in Mathematics |
| spelling | Fruchard, Augustin Verfasser (DE-588)1030057753 aut Composite asymptotic expansions Augustin Fruchard ; Reinhard Schäfke Berlin [u.a.] Springer 2013 X, 161 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Mathematics 2066 Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Schäfke, Reinhard Verfasser (DE-588)1030059276 aut Erscheint auch als Online-Ausgabe 978-3-642-34035-2 Lecture Notes in Mathematics 2066 (DE-604)BV000676446 2066 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4121699&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025497575&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fruchard, Augustin Schäfke, Reinhard Composite asymptotic expansions Lecture Notes in Mathematics Asymptotische Entwicklung (DE-588)4112609-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4112609-9 (DE-588)4020929-5 |
| title | Composite asymptotic expansions |
| title_auth | Composite asymptotic expansions |
| title_exact_search | Composite asymptotic expansions |
| title_full | Composite asymptotic expansions Augustin Fruchard ; Reinhard Schäfke |
| title_fullStr | Composite asymptotic expansions Augustin Fruchard ; Reinhard Schäfke |
| title_full_unstemmed | Composite asymptotic expansions Augustin Fruchard ; Reinhard Schäfke |
| title_short | Composite asymptotic expansions |
| title_sort | composite asymptotic expansions |
| topic | Asymptotische Entwicklung (DE-588)4112609-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Asymptotische Entwicklung Gewöhnliche Differentialgleichung |
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