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Bibliografická citace

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0 (hodnocen0 x )
BK
[Amsterdam?] : Atlantis press, c2015
xvii, 354 s. ; 25 cm

objednat
ISBN 978-94-6239-072-0 (váz.)
Atlantis studies in variational geometry, ISSN 2214-0700 ; vol. 1
Obsahuje bibliografie a rejstřík
000250830
Contents // 1 Jet Prolongations of Fibered Manifolds ... 1 // 1.1 The Rank Theorem ... 1 // 1.2 Fibered Manifolds ... 6 // 1.3 The Contact of Differentiable Mappings ... 10 // 1.4 Jet Prolongations of Fibered Manifolds ... 13 // 1.5 The Horizontalization ... 17 // 1.6 Jet Prolongations of Automorphisms of Fibered Manifolds. ... 20 // 1.7 Jet Prolongations of Vector Fields ... 23 // References ... 33 // 2 Differential Forms on Jet Prolongations of Fibered Manifolds. ... 35 // 2.1 The Contact Ideal ... 35 // 2.2 The Trace Decomposition ... 43 // 2.3 The Horizontalization ... 53 // 2.4 The Canonical Decomposition ... 58 // 2.5 Contact Components and Geometric Operations ... 67 // 2.6 Strongly Contact Forms ... 68 // 2.7 Fibered Homotopy Operators on Jet Prolongations of Fibered Manifolds ... 74 // References ... 84 // 3 Formal Divergence Equations ... 85 // 3.1 Formal Divergence Equations ... 85 // 3.2 Integrability of Formal Divergence Equations ... 89 // 3.3 Projectable Extensions of Differential Forms ... 93 // Reference ... 101 // 4 Variational Structures ... 103 // 4.1 Variational Structures on Fibered Manifolds ... 104 // 4.2 Variational Derivatives ... 108 // 4.3 Lepage Forms ... 112 // 4.4 Euler-Lagrange Forms ... 123 // 4.5 Lepage Equivalents and the Euler-Lagrange Mapping ... 124 // 4.6 The First Variation Formula ... 129 // 4.7 Extremals ... 130 // 4.8 Trivial Lagrangians ... 133 // 4.9 Source Forms and the Vainberg-Tonti Lagrangians ... 135 // 4.10 The Inverse Problem of the Calculus of Variations ... 146 // 4.11 Local Variationality of Second-Order Source Forms ... 157 // References ... 166 // 5 Invariant Variational Structures ... 169 // 5.1 Invariant Differential Forms ... 170 // 5.2 Invariant Lagrangians and Conservation Equations ... 172 // 5.3 Invariant Euler-Lagrange Forms ... 177 // 5.4 Symmetries of Extremals and Jacobi Vector Fields ... 178 // References ... 185 //
6 Examples: Natural Lagrange Structures ... 187 // 6.1 The Hilbert Variational Functional ... 188 // 6.2 Natural Lagrange Structures ... 194 // 6.3 Connections ... 197 // References ... 200 // 7 Elementary Sheaf Theory ... 201 // 7.1 Sheaf Spaces ... 201 // 7.2 Abelian Sheaf Spaces ... 207 // 7.3 Sections of Abelian Sheaf Spaces ... 211 // 7.4 Abelian Presheaves ... 213 // 7.5 Sheaf Spaces Associated with Abelian Presheaves ... 217 // 7.6 Sheaves Associated with Abelian Presheaves ... 221 // 7.7 Sequences of Abelian Groups, Complexes ... 226 // 7.8 Exact Sequences of Abelian Sheaves ... 238 // 7.9 Cohomology Groups of a Sheaf ... 242 // 7.10 Sheaves over Paracompact Hausdorff Spaces ... 250 // References ... 261 // 8 Variational Sequences ... 263 // 8.1 The Contact Sequence ... 264 // 8.2 The Variational Sequence ... 272 // 8.3 Variational Projectors ... 273 // 8.4 The Euler-Lagrange Morphisms ... 288 // 8.5 Variationally Trivial Lagrangians ... 296 // 8.6 Global Inverse Problem of the Calculus of Variations ... 298 // References ... 300 // Appendix: Analysis on Euclidean Spaces and Smooth Manifolds ... 303 // Bibliography ... 341 // Index ...347

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