Painlevé differential equations in the complex plane:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
de Gruyter
2002
|
| Series: | De Gruyter studies in mathematics
28 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. [283]-299) and index |
| Physical Description: | VIII, 303 S. |
| ISBN: | 3110173794 |
Staff View
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Record in the Search Index
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| adam_text | VALERII I. GROMAK * ILPO LAINE * SHUN SHIMOMURA PAINLEVE DIFFERENTIAL
EQUATIONS IN THE COMPLEX PLANE W DE G WALTER DE GRUYTER BERLIN * NEW
YORK 2002 CONTENTS INTRODUCTION 1 1 MEROMORPHIC NATURE OF SOLUTIONS 5 §1
THE FIRST PAINLEVE EQUATION (PI) 5 §2 THE SECOND PAINLEVE EQUATION (P 2
) 11 §3 THE THIRD PAINLEVE EQUATION (P3) 21 §4 THE FOURTH PAINLEVE
EQUATION (P4) 22 §5 THE FIFTH PAINLEVE EQUATION (P 5 ) 29 §6 THE SIXTH
PAINLEVE EQUATION (P(,) 30 2 GROWTH OF PAINLEVE TRANSCENDENTS 32 §7
GROWTH OF FIRST PAINLEVE TRANSCENDENTS 32 §8 GROWTH OF SECOND AND FOURTH
PAINLEVE TRANSCENDENTS 45 §9 GROWTH OF THIRD AND FIFTH PAINLEVE
TRANSCENDENTS 54 3 VALUE DISTRIBUTION OF PAINLEVE TRANSCENDENTS 55 §10
DEFICIENCIES AND RAMIFICATION INDICES 55 § 11 THE SECOND MAIN THEOREM
FOR PAINLEVE TRANSCENDENTS 69 §12 VALUE DISTRIBUTION WITH RESPECT TO
SMALL TARGET FUNCTIONS 72 4 THE FIRST PAINLEVE EQUATION (PI) 78 §13
NONEXISTENCE OF THE FIRST INTEGRALS 78 §14 REPRESENTATION OF SOLUTIONS
AS QUOTIENT OF ENTIRE FUNCTIONS 80 § 15 SPECIAL EXPANSIONS OF SOLUTIONS
83 §16 HIGHER ORDER ANALOGUES OF (PI) 87 5 THE SECOND PAINLEVE EQUATION
(P2) 94 §17 CANONICAL REPRESENTATION OF SOLUTIONS 94 § 18 POLES OF
SECOND PAINLEVE TRANSCENDENTS 97 §19 THE BACKHAND TRANSFORMATIONS OF (P
2 ) 100 §20 RATIONAL SOLUTIONS OF (P 2 ) 104 §21 THE AIRY SOLUTIONS OF
(P 2 ) 108 §22 HIGHER ORDER ANALOGUES OF (P 2 ) 112 6 THE FOURTH
PAINLEVE EQUATION (P 4 ) 121 §23 PRELIMINARY REMARKS 121 §24 POLES OF
FOURTH PAINLEVE TRANSCENDENTS 124 §25 CONNECTION FORMULAE BETWEEN
SOLUTIONS OF (P4) 125 §26 RATIONAL SOLUTIONS OF (P 4 ) 135 VIII CONTENTS
§27 THE COMPLEMENTARY ERROR FUNCTION HIERARCHY 141 §28 A HALF-INTEGER
HIERARCHY OF SOLUTIONS 144 7 THE THIRD PAINLEVE EQUATION (P 3 ) 146 §29
PRELIMINARY REMARKS 146 §30 BEHAVIOR OF SOLUTIONS AROUND Z = 0 AND Z =
OO 151 §31 POLES OF THIRD PAINLEVE TRANSCENDENTS 157 §32 CANONICAL
REPRESENTATION OF SOLUTIONS 160 §33 THE SPECIAL CASE Y = 0, AS ^ 0 162
§34 CONNECTION BETWEEN SOLUTIONS OF (P3) AND (P5) 168 §35 RATIONAL AND
CLASSICAL TRANSCENDENTAL SOLUTIONS OF (P3) WHEN YS ^ 0 . 173 8 THE FIFTH
PAINLEVE EQUATION (P 5 ) 178 §36 PRELIMINARY OBSERVATIONS 178 §37 THE
BEHAVIOR OF SOLUTIONS NEAR Z = 0 AND Z = 00 183 §38 THE SPECIAL CASE 5
= 0, Y ^ 0 189 §39 THE BACKHAND TRANSFORMATIONS OF (P 5 ) 193 §40
RATIONAL AND ONE-PARAMETER FAMILIES OF SOLUTIONS 203 §41 CONNECTION
BETWEEN (P3) AND (P5) REVISITED 208 9 THE SIXTH PAINLEVE EQUATION (PE)
211 §42 GENERAL PROPERTIES OF SOLUTIONS 211 §43 PAIRS OF DIFFERENTIAL
EQUATIONS EQUIVALENT TO (PQ) 216 §44 A RICCATI DIFFERENTIAL EQUATION
RELATED TO (P^) 221 §45 A FIRST ORDER ALGEBRAIC DIFFERENTIAL EQUATION
RELATED TO (P6) 225 §46 SINGULAR POINTS OF SOLUTIONS OF (P^) 228 §47
CONNECTION FORMULAE BETWEEN SOLUTIONS OF (PG) 232 §48 ELEMENTARY
SOLUTIONS OF (P6) 237 10 APPLICATIONS OF PAINLEVE EQUATIONS 247 §49
PARTIAL DIFFERENTIAL EQUATIONS RELATED TO PAINLEVE EQUATIONS 247 §50
DISCRETE PAINLEVE EQUATIONS 261 APPENDIX A LOCAL EXISTENCE AND
UNIQUENESS OF SOLUTIONS OF COMPLEX DIFFERENTIAL EQUATIONS 267 APPENDIX B
BASIC NOTATIONS AND FACTS IN THE NEVANLINNA THEORY 274 BIBLIOGRAPHY 283
INDEX 301
|
| any_adam_object | 1 |
| author | Gromak, Valerij I. Laine, Ilpo Shimomura, Shun |
| author_facet | Gromak, Valerij I. Laine, Ilpo Shimomura, Shun |
| author_role | aut aut aut |
| author_sort | Gromak, Valerij I. |
| author_variant | v i g vi vig i l il s s ss |
| building | Verbundindex |
| bvnumber | BV019688857 |
| callnumber-first | Q - Science |
| callnumber-label | QA372 |
| callnumber-raw | QA372 |
| callnumber-search | QA372 |
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| classification_rvk | SK 500 |
| ctrlnum | (OCoLC)50322775 (DE-599)BVBBV019688857 |
| dewey-full | 515/.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019688857 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:03:52Z |
| institution | BVB |
| isbn | 3110173794 |
| language | English |
| lccn | 2002031158 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013016704 |
| oclc_num | 50322775 |
| open_access_boolean | |
| owner | DE-20 DE-634 DE-188 DE-824 |
| owner_facet | DE-20 DE-634 DE-188 DE-824 |
| physical | VIII, 303 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Gromak, Valerij I. Verfasser aut Painlevé differential equations in the complex plane Valerii I. Gromak ; Ilpo Laine ; Shun Shimomura Berlin [u.a.] de Gruyter 2002 VIII, 303 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 28 Includes bibliographical references (p. [283]-299) and index Complexe variabelen gtt Fonctions d'une variable complexe Painlevé, Équations de Painlevé-vergelijkingen gtt Functions of complex variables Painlevé equations Komplexe Funktion (DE-588)4217733-9 gnd rswk-swf Painlevé-Gleichung (DE-588)4123902-7 gnd rswk-swf Painlevé-Gleichung (DE-588)4123902-7 s Komplexe Funktion (DE-588)4217733-9 s DE-604 Laine, Ilpo Verfasser aut Shimomura, Shun Verfasser aut De Gruyter studies in mathematics 28 (DE-604)BV000005407 28 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013016704&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gromak, Valerij I. Laine, Ilpo Shimomura, Shun Painlevé differential equations in the complex plane De Gruyter studies in mathematics Complexe variabelen gtt Fonctions d'une variable complexe Painlevé, Équations de Painlevé-vergelijkingen gtt Functions of complex variables Painlevé equations Komplexe Funktion (DE-588)4217733-9 gnd Painlevé-Gleichung (DE-588)4123902-7 gnd |
| subject_GND | (DE-588)4217733-9 (DE-588)4123902-7 |
| title | Painlevé differential equations in the complex plane |
| title_auth | Painlevé differential equations in the complex plane |
| title_exact_search | Painlevé differential equations in the complex plane |
| title_full | Painlevé differential equations in the complex plane Valerii I. Gromak ; Ilpo Laine ; Shun Shimomura |
| title_fullStr | Painlevé differential equations in the complex plane Valerii I. Gromak ; Ilpo Laine ; Shun Shimomura |
| title_full_unstemmed | Painlevé differential equations in the complex plane Valerii I. Gromak ; Ilpo Laine ; Shun Shimomura |
| title_short | Painlevé differential equations in the complex plane |
| title_sort | painleve differential equations in the complex plane |
| topic | Complexe variabelen gtt Fonctions d'une variable complexe Painlevé, Équations de Painlevé-vergelijkingen gtt Functions of complex variables Painlevé equations Komplexe Funktion (DE-588)4217733-9 gnd Painlevé-Gleichung (DE-588)4123902-7 gnd |
| topic_facet | Complexe variabelen Fonctions d'une variable complexe Painlevé, Équations de Painlevé-vergelijkingen Functions of complex variables Painlevé equations Komplexe Funktion Painlevé-Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013016704&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
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