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Titlebook: Singularities and Groups in Bifurcation Theory; Volume II Martin Golubitsky,Ian Stewart,David G. Schaeffer Book 1988 Springer-Verlag New Yo

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書目名稱Singularities and Groups in Bifurcation Theory
副標題Volume II
編輯Martin Golubitsky,Ian Stewart,David G. Schaeffer
視頻videohttp://file.papertrans.cn/868/867922/867922.mp4
叢書名稱Applied Mathematical Sciences
圖書封面Titlebook: Singularities and Groups in Bifurcation Theory; Volume II Martin Golubitsky,Ian Stewart,David G. Schaeffer Book 1988 Springer-Verlag New Yo
描述Bifurcation theory studies how the structure of solutions to equations changes as parameters are varied. The nature of these changes depends both on the number of parameters and on the symmetries of the equations. Volume I discusses how singularity-theoretic techniques aid the understanding of transitions in multiparameter systems. This volume focuses on bifurcation problems with symmetry and shows how group-theoretic techniques aid the understanding of transitions in symmetric systems. Four broad topics are covered: group theory and steady-state bifurcation, equicariant singularity theory, Hopf bifurcation with symmetry, and mode interactions. The opening chapter provides an introduction to these subjects and motivates the study of systems with symmetry. Detailed case studies illustrate how group-theoretic methods can be used to analyze specific problems arising in applications.
出版日期Book 1988
關鍵詞Group theory; Irreducibility; Lattice; group action; invariant theory; partial differential equation
版次1
doihttps://doi.org/10.1007/978-1-4612-4574-2
isbn_softcover978-1-4612-8929-6
isbn_ebook978-1-4612-4574-2Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer-Verlag New York, Inc. 1988
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Symmetry-Breaking in Steady-State Bifurcation,tion of a compact Lie group Γ on . ?.. Steady-state solutions satisfy . 0; that is, . We focus here on the symmetries that a solution . may possess and in particular define some simple “geometric” notions that will prove to be of central importance.
板凳
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,The Planar Bénard Problem,vitational field; motion occurs because hotter fluid is less dense and therefore tends to rise. In this Case Study we consider only carefully controlled laboratory experiments in which a horizontal layer of fluid is heated from below and the ensuing motion is observed. Of course, such experiments ar
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,The Traction Problem for Mooney—Rivlin Material,pontaneous symmetry-breaking and to describe the kinds of results that can be obtained by a singularity-theoretic analysis. This case study has a different aim: to present complete calculations supporting the singularity theory analysis of a specific bifurcation problem. The Rivlin cube is an ideal
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Further Examples of Hopf Bifurcation with Symmetry,al group symmetry ., systems with .(3) symmetry (corresponding to any irreducible representation), and systems with the symmetry . +? . of the hexagonal lattice. For . and . +? . we consider the stability of bifurcating branches. These examples illustrate several features of specific applications th
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