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Dynamics and Symmetry
Michael J. FieldMike Field
出版Imperial College Press, 2007
主題Mathematics / Differential Equations / GeneralScience / Physics / General
ISBN18609485459781860948541
URLhttp://books.google.com.hk/books?id=V69gDQAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋This book contains the first systematic exposition of the global and local theory of dynamics equivariant with respect to a (compact) Lie group. Aside from general genericity and normal form theorems on equivariant bifurcation, it describes many general families of examples of equivariant bifurcation and includes a number of novel geometric techniques, in particular, equivariant transversality. This important book forms a theoretical basis of future work on equivariant reversible and Hamiltonian systems. This book also provides a general and comprehensive introduction to codimension one equivariant bifurcation theory. In particular, it includes the bifurcation theory developed with Roger Richardson on subgroups of reflection groups and the Maximal Isotropy Subgroup Conjecture. A number of general results are also given on the global theory. Introductory material on groups, representations and G -manifolds are covered in the first three chapters of the book. In addition, a self-contained introduction of equivariant transversality is given, including necessary results on stratifications as well as results on equivariant jet transversality developed by Edward Bierstone. Sample Chapter(s). Chapter 1: Groups (309 KB). Contents: Groups; Group Actions and Representations; Smooth G -manifolds; Equivariant Bifurcation Theory: Steady State Bifurcation; Equivariant Bifurcation Theory: Dynamics; Equivariant Transversality; Applications of G -transversality to Bifurcation Theory I; Equivariant Dynamics; Dynamical Systems on G -manifolds; Applications of G -transversality to Bifurcation Theory II. Readership: Academics and graduate students in pure and applied mathematics.