Dynamics and Symmetry
By addebook • Jul 14th, 2008 • Category: Mathematics •
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Dynamics and Symmetry (Icp Advanced Texts in Mathematics) (Icp Advanced Texts in Mathematics)
Dynamics and Symmetry (Icp Advanced Texts in Mathematics) (Icp Advanced Texts in Mathematics)
By Michael J. Field
Publisher: Imperial College Press
Number Of Pages: 492
Publication Date: 2007-09-03
ISBN-10 / ASIN: 1860948286
ISBN-13 / EAN: 9781860948282
Binding: Hardcover
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.
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