Composite asymptotic expansions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
|
| Series: | Lecture Notes in Mathematics
2066 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | X, 161 S. graph. Darst. |
| ISBN: | 3642340342 9783642340345 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV040671010 | ||
| 003 | DE-604 | ||
| 005 | 20130219 | ||
| 007 | t | ||
| 008 | 130114s2013 d||| |||| 00||| eng d | ||
| 015 | |a 12N38 |2 dnb | ||
| 016 | 7 | |a 1025944380 |2 DE-101 | |
| 020 | |a 3642340342 |c : Pb. : EUR 37.40 (DE) |9 3-642-34034-2 | ||
| 020 | |a 9783642340345 |c : Pb. : EUR 37.40 (DE) |9 978-3-642-34034-5 | ||
| 035 | |a (OCoLC)829219384 | ||
| 035 | |a (DE-599)DNB1025944380 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-188 |a DE-824 |a DE-91G |a DE-11 |a DE-83 | ||
| 082 | 0 | |a 511.4 |2 22/ger | |
| 084 | |a SI 850 |0 (DE-625)143199: |2 rvk | ||
| 084 | |a MAT 346f |2 stub | ||
| 084 | |a 34M30 |2 msc | ||
| 084 | |a 41A60 |2 msc | ||
| 100 | 1 | |a Fruchard, Augustin |e Verfasser |0 (DE-588)1030057753 |4 aut | |
| 245 | 1 | 0 | |a Composite asymptotic expansions |c Augustin Fruchard ; Reinhard Schäfke |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a X, 161 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture Notes in Mathematics |v 2066 | |
| 650 | 0 | 7 | |a Asymptotische Entwicklung |0 (DE-588)4112609-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Asymptotische Entwicklung |0 (DE-588)4112609-9 |D s |
| 689 | 0 | 1 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Schäfke, Reinhard |e Verfasser |0 (DE-588)1030059276 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-642-34035-2 |
| 830 | 0 | |a Lecture Notes in Mathematics |v 2066 |w (DE-604)BV000676446 |9 2066 | |
| 856 | 4 | |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=4121699&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-025497575 | |
Record in the Search Index
| _version_ | 1807954797916061696 |
|---|---|
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV040671010</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20130219</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">130114s2013 d||| |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">12N38</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1025944380</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3642340342</subfield><subfield code="c">: Pb. : EUR 37.40 (DE)</subfield><subfield code="9">3-642-34034-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642340345</subfield><subfield code="c">: Pb. : EUR 37.40 (DE)</subfield><subfield code="9">978-3-642-34034-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)829219384</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1025944380</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-188</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.4</subfield><subfield code="2">22/ger</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 850</subfield><subfield code="0">(DE-625)143199:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 346f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">34M30</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">41A60</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Fruchard, Augustin</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1030057753</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Composite asymptotic expansions</subfield><subfield code="c">Augustin Fruchard ; Reinhard Schäfke</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2013</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 161 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Lecture Notes in Mathematics</subfield><subfield code="v">2066</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Asymptotische Entwicklung</subfield><subfield code="0">(DE-588)4112609-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4020929-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Asymptotische Entwicklung</subfield><subfield code="0">(DE-588)4112609-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4020929-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Schäfke, Reinhard</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1030059276</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-642-34035-2</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture Notes in Mathematics</subfield><subfield code="v">2066</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">2066</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="q">text/html</subfield><subfield code="u">http://deposit.dnb.de/cgi-bin/dokserv?id=4121699&prov=M&dok_var=1&dok_ext=htm</subfield><subfield code="3">Inhaltstext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-025497575</subfield></datafield></record></collection> |
| id | DE-604.BV040671010 |
| illustrated | Illustrated |
| indexdate | 2024-08-21T00:27:35Z |
| institution | BVB |
| isbn | 3642340342 9783642340345 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025497575 |
| oclc_num | 829219384 |
| open_access_boolean | |
| owner | DE-188 DE-824 DE-91G DE-BY-TUM DE-11 DE-83 |
| owner_facet | DE-188 DE-824 DE-91G DE-BY-TUM DE-11 DE-83 |
| 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 |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4121699&prov=M&dok_var=1&dok_ext=htm 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 |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT fruchardaugustin compositeasymptoticexpansions AT schafkereinhard compositeasymptoticexpansions |