Cohomological analysis of partial differential equations and secondary calculus:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2001
|
| Schriftenreihe: | Translations of mathematical monographs
204 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem. Russ. übers. |
| Beschreibung: | XV, 247 S. |
| ISBN: | 082182922X |
Internformat
MARC
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| 100 | 1 | |a Vinogradov, Aleksandr M. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Kogomologiceskij analiz differencial'nych uravnenij v castnych proizvodnych i vtoricnoe iscislenie |
| 245 | 1 | 0 | |a Cohomological analysis of partial differential equations and secondary calculus |c A. M. Vinogradov |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2001 | |
| 300 | |a XV, 247 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 204 | |
| 500 | |a Aus dem. Russ. übers. | ||
| 650 | 4 | |a Differential equations, Nonlinear | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Homology theory | |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
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| 689 | 0 | 2 | |a Homologietheorie |0 (DE-588)4141714-8 |D s |
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| 830 | 0 | |a Translations of mathematical monographs |v 204 |w (DE-604)BV000002394 |9 204 | |
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Datensatz im Suchindex
| _version_ | 1804129749592702976 |
|---|---|
| adam_text | Contents
Foreword
vii
Introduction
ix
Chapter
0.
From Symmetries of Partial Differential Equations
to Secondary Calculus
1
0.1.
What are symmetries of partial differential equations,
and what are partial differential equations themselves?
2
0.2.
Jets
3
0.3.
Higher-order contact structures
5
0.4.
Differential equations are
diŕHeties
6
0.5.
What are symmetries of partial differential equations?
8
0.6.
Infinitesimal symmetries of partial differential equations are secondary
quantized vector fields
10
0.7.
Digression: on symmetries of partial differential equations
12
0.8.
Secondary ( quantized ) functions
14
0.9.
Higher-order scalar secondary ( quantized ) operators
16
0.10.
Secondary ( quantized ) differential forms and C-spectral sequences
19
0.11.
How does the
С
-spectral sequence work?
21
Chapter
1.
Elements of Differential Calculus
in Commutative Algebras
25
1.1.
General preliminaries
25
1.2.
Adjoint operators
31
1.3.
Spencer complexes and the Green formula
38
1.4.
Quadratic Lagrangians and the
Euler
operator
44
1.5.
Conservation laws in the linear theory
47
1.6.
Automorphisms and the linear Noether theorem
51
1.7.
Concluding remarks
55
Chapter
2.
Geometry of Finite-Order Contact Structures
and the Classical Theory of Symmetries
of Partial Differential Equations
57
2.1.
Necessary facts from the geometry of jet spaces
57
2.2.
The structure of [/-transformations
66
2.3.
Infinitesimal automorphisms of the Cartan distribution
72
2.4.
The structure of automorphisms of the Cartan distribution
on the manifolds Jk(E,m),
к
<
oo
80
2.5.
Classical theory of symmetries of partial differential equations
86
2.6.
Concluding remarks
93
Chapter
3.
Geometry of Infinitely Prolonged Differential
Equations and Higher Symmetries
95
3.1.
Geometry of infinitely prolonged equations,
and related differential calculus
95
3.2.
Horizontalization operation, the structure of Cartan
submodules
and of C-differential operators
100
3.3.
Higher infinitesimal symmetries of differential equations
107
3.4.
The structure of C-transformations
113
3.5.
Examples of diffieties
122
3.6.
Concluding remarks
125
Chapter
4.
C-spectral Sequence and Some Applications
127
4.1.
Spencer complexes and the Green formula in the C-theory
127
4.2.
Nonlinear Lagrangian formalism
133
4.3.
The
С
-spectral sequence
137
4.4.
The
С
-spectral sequence of infinitely prolonged equations
155
4.5.
Applications to the Lagrangian formalism with constraints
and to the theory of conservation laws
172
4.6.
Characteristic classes
182
4.7.
Concluding remarks
187
Chapter
5.
Introduction to Secondary Calculus
189
5.1.
First idea of Secondary Calculus
189
5.2.
Secondary linear algebra
196
5.3.
Secondary modules
203
5.4.
Secondary linear differential operators
210
5.5.
Cy-spectral sequence
213
5.6.
Secondary multivector-valued differential forms
221
5.7.
The secondary
Frölicher-Nijenhuis
formalism
227
5.8.
Concluding remarks
233
Bibliography
237
|
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| dewey-full | 515/.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV016404454 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:10:05Z |
| institution | BVB |
| isbn | 082182922X |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010146498 |
| oclc_num | 47296188 |
| open_access_boolean | |
| owner | DE-703 DE-739 |
| owner_facet | DE-703 DE-739 |
| physical | XV, 247 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Vinogradov, Aleksandr M. Verfasser aut Kogomologiceskij analiz differencial'nych uravnenij v castnych proizvodnych i vtoricnoe iscislenie Cohomological analysis of partial differential equations and secondary calculus A. M. Vinogradov Providence, RI American Math. Soc. 2001 XV, 247 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 204 Aus dem. Russ. übers. Differential equations, Nonlinear Geometry, Differential Homology theory Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Homologietheorie (DE-588)4141714-8 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Differentialgeometrie (DE-588)4012248-7 s Homologietheorie (DE-588)4141714-8 s DE-604 Translations of mathematical monographs 204 (DE-604)BV000002394 204 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010146498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vinogradov, Aleksandr M. Cohomological analysis of partial differential equations and secondary calculus Translations of mathematical monographs Differential equations, Nonlinear Geometry, Differential Homology theory Differentialgeometrie (DE-588)4012248-7 gnd Homologietheorie (DE-588)4141714-8 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4141714-8 (DE-588)4128900-6 |
| title | Cohomological analysis of partial differential equations and secondary calculus |
| title_alt | Kogomologiceskij analiz differencial'nych uravnenij v castnych proizvodnych i vtoricnoe iscislenie |
| title_auth | Cohomological analysis of partial differential equations and secondary calculus |
| title_exact_search | Cohomological analysis of partial differential equations and secondary calculus |
| title_full | Cohomological analysis of partial differential equations and secondary calculus A. M. Vinogradov |
| title_fullStr | Cohomological analysis of partial differential equations and secondary calculus A. M. Vinogradov |
| title_full_unstemmed | Cohomological analysis of partial differential equations and secondary calculus A. M. Vinogradov |
| title_short | Cohomological analysis of partial differential equations and secondary calculus |
| title_sort | cohomological analysis of partial differential equations and secondary calculus |
| topic | Differential equations, Nonlinear Geometry, Differential Homology theory Differentialgeometrie (DE-588)4012248-7 gnd Homologietheorie (DE-588)4141714-8 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Differential equations, Nonlinear Geometry, Differential Homology theory Differentialgeometrie Homologietheorie Nichtlineare partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010146498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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