Global properties of linear ordinary differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1991
|
| Series: | Mathematics and its applications / East European series
52 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [299] - 314 |
| Physical Description: | XV, 320 S. graph. Darst. |
| ISBN: | 0792312694 |
Staff View
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| 245 | 1 | 0 | |a Global properties of linear ordinary differential equations |c František Neuman |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 1991 | |
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| 650 | 4 | |a Differential equations | |
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Record in the Search Index
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| adam_text | Contents
Preface xi
Symbols defined in the text xiii
1. Introduction with historical remarks 1
2. Notation, definitions and some basic facts 5
2.1 Generalities 5
2.2 Maps 6
2.3 Topology 8
2.4 Algebraic structures 9
2.5 Vector spaces 16
2.6 Linear differential equations 18
2.7 Functional equations 22
3. Global transformations 25
3.1 Definition of the global transformations 25
3.2 Smoothness of global transformations 33
3.3 Algebraic approach to global transformations 38
3.4 Fundamental problems 46
4. Analytic, algebraic and geometrical aspects of global transformations 49
4.1 Some useful formulas 49
4.2 Global transformations of special classes of linear differential
equations 52
4.3 Covariant constructions of linear differential equations ... 57
4.4 Geometrical approach to global transformations 69
viii contents
5. Criterion of global equivalence 73
5.1 Boruvka s criterion of global equivalence of the second
order equations 74
5.2 Criterion of global equivalence of the third and higher
order equations 80
6. Stationary groups 87
6.1 Notation and preliminary results 88
6.2 Preparatory results 89
6.3 Subgroups of stationary groups with increasing elements . . 99
6.4 Stationary groups with decreasing elements 106
6.5 Complete list of stationary groups and characterization of the 109
corresponding equations
7. Canonical forms 123
7.1 Notion of canonical forms 123
7.2 The Laguerre Forsyth and Halphen forms 124
7.3 Cartan s moving frame of reference method 133
7.4 Hereditary property 140
7.5 Global canonical forms: geometrical approach 146
7.6 Global canonical forms: analytic approach 159
7.7 List of canonical forms of the second and third order equations 162
8. Invariants 165
8.1 Notion of invariant and covariant 165
8.2 Covariants 167
8.3 Local invariants and covariants 169
8.4 Global invariants 172
8.5 Smoothness of coefficients as an invariant 173
9. Equations with solutions of prescribed properties 185
9.1 Coordinate approach 185
9.2 Asymptotic properties of solutions of the second order
equations 189
9.3 Periodic solutions of the second order equations 194
9.4 Geometrical approach 213
10. Zeros of solutions 215
10.1 Notation and definitions 215
10.2 Representation of zeros 217
10.3 Second order equations 223
CONTENTS ix
10.4 Third order equations 230
10.5 Iterative «th order equations 248
10.6 Periodic solutions of nth order equations 250
11. Related results and some applications 255
11.1 Asymptotic properties and zeros of solutions of second order
equations 255
11.2 Integral inequalities 262
11.3 Affine geometry of plane curves 264
11.4 Isoperimetric theorems 278
11.5 Related results and comments, possible trends of further
research 285
12. Appendix: Two functional equations 293
12.1 Abel functional equation 293
12.2 Euler functional equation for homogeneous functions. . . . 298
Literature cited in the book and/or for supplementary reading .... 299
Subject index 315
Index of names 318
|
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| id | DE-604.BV008230611 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:16:43Z |
| institution | BVB |
| isbn | 0792312694 |
| language | English |
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| physical | XV, 320 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series2 | Mathematics and its applications / East European series |
| spelling | Neuman, František Verfasser aut Global properties of linear ordinary differential equations František Neuman Dordrecht [u.a.] Kluwer Acad. Publ. 1991 XV, 320 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / East European series 52 Literaturverz. S. [299] - 314 Equations différentielles ram Transformations (Mathématiques) ram Differential equations Transformations (Mathematics) Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd rswk-swf Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 s DE-604 East European series Mathematics and its applications 52 (DE-604)BV000006709 52 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005432356&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Neuman, František Global properties of linear ordinary differential equations Equations différentielles ram Transformations (Mathématiques) ram Differential equations Transformations (Mathematics) Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd |
| subject_GND | (DE-588)4353441-7 |
| title | Global properties of linear ordinary differential equations |
| title_auth | Global properties of linear ordinary differential equations |
| title_exact_search | Global properties of linear ordinary differential equations |
| title_full | Global properties of linear ordinary differential equations František Neuman |
| title_fullStr | Global properties of linear ordinary differential equations František Neuman |
| title_full_unstemmed | Global properties of linear ordinary differential equations František Neuman |
| title_short | Global properties of linear ordinary differential equations |
| title_sort | global properties of linear ordinary differential equations |
| topic | Equations différentielles ram Transformations (Mathématiques) ram Differential equations Transformations (Mathematics) Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd |
| topic_facet | Equations différentielles Transformations (Mathématiques) Differential equations Transformations (Mathematics) Lineare gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005432356&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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