Painlevé equations through symmetry:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2004
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| Series: | Translations of mathematical monographs
223 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 156 S. graph. Darst. |
| ISBN: | 0821832212 |
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MARC
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Record in the Search Index
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| adam_text | TRANSLATIONS OF MATHEMATICAL MONOGRAPHS VOLUME 223 PAINLEVE EQUATIONS
THROUGH SYMMETRY MASATOSHI NOUMI TRANSLATED BY MASATOSHI NOUMI &//I.^ S
^ | AMERICAN MATHEMATICAL SOCIETY ! PROVIDENCE, RHODE ISLAND CONTENTS
PREFACE V PREFACE TO THE ENGLISH EDITION IX CHAPTER 1. WHAT IS A
BACKLUND TRANSFORMATION? 1 1.1. HAMILTONIAN REPRESENTATION OF PN 1 1.2.
IMMEDIATELY ACCESSIBLE SOLUTIONS 3 1.3. BACKLUND TRANSFORMATIONS 5 1.4.
COMPOSING BACKLUND TRANSFORMATIONS 6 1.5. GENERATING SOLUTIONS 9 1.6.
PICTURE OF CLASSICAL SOLUTIONS 11 CHAPTER 2. THE SYMMETRIC FORM 13 2.1.
THE SYMMETRIC FORM OF PIV 13 2.2. FUNDAMENTAL SPECIAL SOLUTIONS 14 2.3.
AFFINE WEYL GROUP 17 2.4. BACKLUND TRANSFORMATIONS 21 2.5. THE SYMMETRIC
FORM OF PN 24 CHAPTER 3. R-FUNCTIONS 27 3.1. POISSON STRUCTURE AND THE
HAMILTONIAN SYSTEM 27 3.2. R-FUNCTIONS AND THEIR DIFFERENTIAL EQUATIONS
31 3.3. BACKLUND TRANSFORMATIONS OF THE R-FUNCTIONS 35 3.4. VARIOUS
RELATIONS AMONG THE R-FUNCTIONS 38 3.5. R-FUNCTIONS FOR PN 40 CHAPTER 4.
R-FUNCTIONS ON THE LATTICE 45 4.1. THE LATTICE FOR P N 45 4.2. THE
LATTICE FOR P IV 49 4.3. (^-FACTORS AND OKAMOTO POLYNOMIALS 54 4.4.
DISCRETE SYSTEM OF TYPE A N !_I 57 4.5. R-FUNCTIONS ON THE A N -
LATTICE 62 CHAPTER 5. JACOBI-TRUDI FORMULA 67 5.1. YOUNG DIAGRAMS AND
MAYA DIAGRAMS 67 5.2. FORMULAS OF JACOBI-TRUDI TYPE 71 5.3. EXAMPLES OF
PJY AND PN 76 5.4. SCHUR FUNCTIONS AND ^-FACTORS 78 CHAPTER 6. GETTING
FAMILIAR WITH DETERMINANTS 85 6.1. BASIC PROPERTIES OF MINOR
DETERMINANTS 85 IV CONTENTS 6.2. GAUSS DECOMPOSITION AND THE JACOBI
IDENTITY 87 6.3. DIAGONALIZATION OF TRIANGULAR MATRICES 93 6.4. PLIICKER
RELATIONS 95 CHAPTER 7. GAUSS DECOMPOSITION AND BIRATIONAL
TRANSFORMATIONS 99 7.1. BIRATIONAL TRANSFORMATION OF THE / VARIABLES 99
7.2. BIRATIONAL TRANSFORMATIONS ARISING FROM THE GAUSS DECOMPOSITION 103
7.3. WHERE ARE THE R-FUNCTIONS? 105 7.4. EXPLICIT FORMULAS OF
JACOBI-TRUDI TYPE 109 7.5. BIRATIONAL TRANSFORMATIONS OF TYPE ^4OO AND
OF TYPE -I4| L _ 1 115 7.6. ACTION OF THE AFFINE WEYL GROUP ON THE MAYA
DIAGRAMS 120 CHAPTER 8. LAX FORMALISM 125 8.1. RELATION WITH LINEAR
ORDINARY DIFFERENTIAL EQUATIONS 125 8.2. SYMMETRIC FORMS OF PN, PIV AND
THE LAX REPRESENTATIONS 129 APPENDIX 133 A.O. PROFILE OF PAINLEVE
EQUATIONS 133 A.I. HAMILTONIAN SYSTEMS [SECTION 1.1] 136 A.2. POISSON
STRUCTURE AND CANONICAL TRANSFORMATIONS [SECTION 1.1] 138 A.3. RICCATI
EQUATIONS [SECTION 1.2] 139 A.4. COMPUTATION OF BACKLUND TRANSFORMATIONS
[SECTIONS 1.5 AND 2.3] 139 A.5. CLASSICAL SOLUTIONS AND INVARIANT
DIVISORS [SECTIONS 1.6 AND 2.2] 142 A.6. SEMIDIRECT PRODUCT OF GROUPS
[SECTION 2.3] 143 A.7. CARTAN MATRICES AND DYNKIN DIAGRAMS [SECTION 2.3]
144 A.8. DEMAZURE OPERATORS [SECTION 2.5] 146 A.9. HIROTA S BILINEAR
OPERATORS [SECTION 3.2] 148 A. 10. APPLICATION OF THE EXTERIOR ALGEBRA
[SECTIONS 6.1 AND 6.4] 149 BIBLIOGRAPHY 153 INDEX 155
|
| any_adam_object | 1 |
| author | Noumi, Masatoshi |
| author_facet | Noumi, Masatoshi |
| author_role | aut |
| author_sort | Noumi, Masatoshi |
| author_variant | m n mn |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 |
| dewey-search | 515.352 |
| dewey-sort | 3515.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV023836667 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:37:43Z |
| institution | BVB |
| isbn | 0821832212 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017478787 |
| oclc_num | 633811779 |
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| physical | IX, 156 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Noumi, Masatoshi Verfasser aut Panruve hoteishiki Painlevé equations through symmetry Masatoshi Noumi Providence, RI American Math. Soc. 2004 IX, 156 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 223 Painlevé-Gleichung (DE-588)4123902-7 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Painlevé-Gleichung (DE-588)4123902-7 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Translations of mathematical monographs 223 (DE-604)BV000002394 223 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478787&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Noumi, Masatoshi Painlevé equations through symmetry Translations of mathematical monographs Painlevé-Gleichung (DE-588)4123902-7 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4123902-7 (DE-588)4020929-5 |
| title | Painlevé equations through symmetry |
| title_alt | Panruve hoteishiki |
| title_auth | Painlevé equations through symmetry |
| title_exact_search | Painlevé equations through symmetry |
| title_full | Painlevé equations through symmetry Masatoshi Noumi |
| title_fullStr | Painlevé equations through symmetry Masatoshi Noumi |
| title_full_unstemmed | Painlevé equations through symmetry Masatoshi Noumi |
| title_short | Painlevé equations through symmetry |
| title_sort | painleve equations through symmetry |
| topic | Painlevé-Gleichung (DE-588)4123902-7 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Painlevé-Gleichung Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478787&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT noumimasatoshi panruvehoteishiki AT noumimasatoshi painleveequationsthroughsymmetry |