Introduction to the algebraic theory of invariants of differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Manchester u.a.
Manchester Univ. Press
1988
|
| Schriftenreihe: | Nonlinear science: theory and applications.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | VI, 169 S. graph. Darst. |
| ISBN: | 0719026695 |
Internformat
MARC
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| 100 | 1 | |a Sibirskij, Konstantin S. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Vvedenie v algebraičeskuju teoriju invariantov differencial'nych uravenij |
| 245 | 1 | 0 | |a Introduction to the algebraic theory of invariants of differential equations |c Konstantin Sergeevich Sibirsky |
| 264 | 1 | |a Manchester u.a. |b Manchester Univ. Press |c 1988 | |
| 300 | |a VI, 169 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Nonlinear science: theory and applications. | |
| 500 | |a Aus d. Russ. übers. | ||
| 655 | 7 | |a Differentialvariante |2 gnd |9 rswk-swf | |
| 689 | 0 | 0 | |a Differentialvariante |A f |
| 689 | 0 | |5 DE-604 | |
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Datensatz im Suchindex
| _version_ | 1804116592101949440 |
|---|---|
| adam_text | Contents
Foreword vii
Introduction 1
1 Tensor notation of differential equation systems 3
2 Definition of the polynomial invariant 4
3 Groups of the linear transformations of phase space 5
4 Invariants of affine transformations of a linear
system. Concept of a polynomial basis of invariants 7
5 Operations on tensors 10
6 The fundamental theorem 12
7 The weight of an invariant 15
8 Aronhold symbolism 16
9 Fundamental symbolic identities 18
10 The Aronhold symbolic method for one system of
the second order 19
11 Affine invariants of a two dimensional system with
quadratic nonlinearities 21
12 Comitants of systems of differential equations 25
13 Affine comitants of a bivariate linear system 26
14 Affine classification of a bivariate linear system 28
15 Topological and geometric classifications of a
bivariate linear system 31
16 Affine comitants of a bivariate system with
quadratic nonlinearities 38
17 Syzygies among affine comitants of system (11.1) 42
18 The minimal polynomial basis of affine invariants of
a quadratic system 52
19 Integral straight lines of a quadratic system 55
20 The affine classification of a quadratic system 60
21 The topological classification of a quadratic system
at a # 0 67
vi Contents
22 Geometric classification of a quadratic system at
a^O 70
23 Topological and geometric classifications of a
quadratic system at a = 0 75
24 Invariants of orthogonal transformations 80
25 Invariants of the group of rotations 84
26 Comitants of a many dimensional system with
quadratic nonlinearities 86
27 Complete systems of invariants 92
28 The case of two dimensional systems. Conversion
to complex variables 94
29 Construction of polynomial bases of the invariants
of the group of rotations 97
30 Unary and binary invariants of the group of
rotations in the complex domain 103
31 Functional bases of invariants in subsets 111
32 Axes and planes of symmetry of the system of
differential equations 114
33 Qualitative analysis in the whole of one system 122
34 The centre and isochronity 126
Appendix 1 Invariants of unitary transformations 138
Appendix 2 Affine invariants and comitants of a system with 143
quadratic nonlinearities
References 159
Author Index 168
Subject Index 170
|
| any_adam_object | 1 |
| author | Sibirskij, Konstantin S. |
| author_facet | Sibirskij, Konstantin S. |
| author_role | aut |
| author_sort | Sibirskij, Konstantin S. |
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| dewey-search | 515.3'55 |
| dewey-sort | 3515.3 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre_facet | Differentialvariante |
| id | DE-604.BV002137871 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:40:57Z |
| institution | BVB |
| isbn | 0719026695 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001402043 |
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| physical | VI, 169 S. graph. Darst. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Manchester Univ. Press |
| record_format | marc |
| series2 | Nonlinear science: theory and applications. |
| spelling | Sibirskij, Konstantin S. Verfasser aut Vvedenie v algebraičeskuju teoriju invariantov differencial'nych uravenij Introduction to the algebraic theory of invariants of differential equations Konstantin Sergeevich Sibirsky Manchester u.a. Manchester Univ. Press 1988 VI, 169 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonlinear science: theory and applications. Aus d. Russ. übers. Differentialvariante gnd rswk-swf Differentialvariante f DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001402043&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sibirskij, Konstantin S. Introduction to the algebraic theory of invariants of differential equations |
| title | Introduction to the algebraic theory of invariants of differential equations |
| title_alt | Vvedenie v algebraičeskuju teoriju invariantov differencial'nych uravenij |
| title_auth | Introduction to the algebraic theory of invariants of differential equations |
| title_exact_search | Introduction to the algebraic theory of invariants of differential equations |
| title_full | Introduction to the algebraic theory of invariants of differential equations Konstantin Sergeevich Sibirsky |
| title_fullStr | Introduction to the algebraic theory of invariants of differential equations Konstantin Sergeevich Sibirsky |
| title_full_unstemmed | Introduction to the algebraic theory of invariants of differential equations Konstantin Sergeevich Sibirsky |
| title_short | Introduction to the algebraic theory of invariants of differential equations |
| title_sort | introduction to the algebraic theory of invariants of differential equations |
| topic_facet | Differentialvariante |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001402043&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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