Methods of Bifurcation Theory

Having presented background material from functional analysis and the qualitative theory of differential equations, this text focuses on the static and dynamic aspects of bifurcation theory, which are of particular pertinence to differential equations. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. Dynamic bifurcation theory is concerned with the changes that occur in the structure of the limit sets of solutions of differential equations as parameters in the vector field are varied.