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＜電子ブック＞
Applications of Lie Groups to Differential Equations / by Peter J. Olver
(Graduate Texts in Mathematics. ISSN:21975612 ; 107)

版	2nd ed. 1993.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1993
本文言語	英語
大きさ	XXVIII, 513 p : online resource
冊子体	Applications of Lie groups to differential equations / Peter J. Olver ; : us : acid-free pap,: gw : acid-free pap
著者標目	*Olver, Peter J author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Group theory LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:System theory LCSH:Control theory FREE:Analysis FREE:Group Theory and Generalizations FREE:Calculus of Variations and Optimization FREE:Systems Theory, Control
一般注記	1 Introduction to Lie Groups -- 1.1. Manifolds -- 1.2. Lie Groups -- 1.3. Vector Fields -- 1.4. Lie Algebras -- 1.5. Differential Forms -- Notes -- Exercises -- 2 Symmetry Groups of Differential Equations -- 2.1. Symmetries of Algebraic Equations -- 2.2. Groups and Differential Equations -- 2.3. Prolongation -- 2.4. Calculation of Symmetry Groups -- 2.5. Integration of Ordinary Differential Equations -- 2.6. Nondegeneracy Conditions for Differential Equations -- Notes -- Exercises -- 3 Group-Invariant Solutions -- 3.1. Construction of Group-Invariant Solutions -- 3.2. Examples of Group-Invariant Solutions -- 3.3. Classification of Group-Invariant Solutions -- 3.4. Quotient Manifolds -- 3.5. Group-Invariant Prolongations and Reduction -- Notes -- Exercises -- 4 Symmetry Groups and Conservation Laws -- 4.1. The Calculus of Variations -- 4.2. Variational Symmetries -- 4.3. Conservation Laws -- 4.4. Noether’s Theorem -- Notes -- Exercises -- 5 Generalized Symmetries -- 5.1. Generalized Symmetries of Differential Equations -- 5.2. Récursion Operators, Master Symmetries and Formal Symmetries -- 5.3. Generalized Symmetries and Conservation Laws -- 5.4. The Variational Complex -- Notes -- Exercises -- 6 Finite-Dimensional Hamiltonian Systems -- 6.1. Poisson Brackets -- 6.2. Symplectic Structures and Foliations -- 6.3. Symmetries, First Integrals and Reduction of Order -- Notes -- Exercises -- 7 Hamiltonian Methods for Evolution Equations -- 7.1. Poisson Brackets -- 7.2. Symmetries and Conservation Laws -- 7.3. Bi-Hamiltonian Systems -- Notes -- Exercises -- References -- Symbol Index -- Author Index Symmetry methods have long been recognized to be of great importance for the study of the differential equations. This book provides a solid introduction to those applications of Lie groups to differential equations which have proved to be useful in practice. The computational methods are presented so that graduate students and researchers can readily learn to use them. Following an exposition of the applications, the book develops the underlying theory. Many of the topics are presented in a novel way, with an emphasis on explicit examples and computations. Further examples, as well as new theoretical developments, appear in the exercises at the end of each chapter Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4612-4350-2

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