Titlebook: Applications of Lie Groups to Differential Equations; Peter J. Olver Textbook 1993Latest edition Springer-Verlag New York, Inc. 1993 CON_D

影响深远

Die Verschiedenen Koordinatensysteme. Section 2.2 investigates the precise definition of a symmetry group of a system of differential equations, which requires knowledge of how the group elements actually transform the solutions. The corresponding infinitesimal method rests on the important concept of “prolonging” a group action to th

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Die Verschiedenen Koordinatensystemely states that the solutions which are invariant under a given .-parameter symmetry group of the system can all be found by solving a system of differential equations involving . fewer independent variables than the original system. In particular, if the number of parameters is one less than the num

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Finite-Dimensional Hamiltonian Systems, of this vast subject, namely the interplay between symmetry groups, conservation laws and reduction in order for systems in Hamiltonian form. The Hamiltonian version of Noether’s theorem has a particularly attractive geometrical flavour, which remains somewhat masked in our previous Lagrangian framework.

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0072-5285 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.978-0-387-95000-6978-1-4612-4350-2Series ISSN 0072-5285 Series E-ISSN 2197-5612

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Symmetry Groups and Conservation Laws,um. This basic principle constitutes the first fundamental result in the study of classical or quantum-mechanical systems with prescribed groups of symmetries. Noether’s method is the principal systematic procedure for constructing conservation laws for complicated systems of partial differential equations.