Applied Equivariant Degree, Differential Equations and Dynamical Systems, vol. 1
The aim of this book is to provide an overview of the technique of equivariant degree in the study of bifurcations of dynamical systems invariant with respect to a group action. The first part summarises a few preliminaries in representation theory, equivariant topology and bordism theory and then develops the theory of equivariant degree, firstly for a general compact Lie group G. Later, a concrete description is developed for groups of the type Γ x S1, where Γ are various subgroups of the group SO(3). The second part shows several examples of the method with the focus on Hopf bifurcations in the ordinary differential and functional differential setting and various kinds of symmetry. The authors also provide an Equivariant Degree Library for Maple and explain its usage in a separate chapter. The book is well organised and can be useful to a wide audience. A reader interested mainly in the applications may find a slight inconvenience in having to wait for more concrete examples until after the general theory is fully developed. An appendix on the classical Brouwer and Leray-Schauder degrees would also be handy for review and comparison.