EAN: 9780387970684

ELEMENTARY STABILITY AND BIFURCATION THEORY - G...

In its most general form bifurcation theory is a theory of asymptotic solutions of nonlinear
equations. By asymptotic solutions we mean  for example  steady solutions  time-periodic
solutions  and quasi-periodic solutions. The purpose of this book is to teach the theory of
bifurcation of asymptotic solutions of evolution problems governed by nonlinear differential
equations. We have written this book for the broadest audience of potentially interested
learners: engineers  biologists  chemists  physicists  mathematicians  economists  and others
whose work involves understanding asymptotic solutions of nonlinear differential equations. To
accomplish our aims  we have thought it necessary to make the analysis: (1) general enough to
apply to the huge variety of applications which arise in science and technology  and (2) simple
enough so that it can be understood by persons whose mathe­ matical training does not extend
beyond the classical methods of analysis which were popular in the nineteenth century. Of
course  it is not possible to achieve generality and simplicity in a perfect union but  in fact
the general theory is simpler than the detailed theory required for particular applications.
The general theory abstracts from the detailed problems only the essential features and
provides the student with the skeleton on which detailed structures of the applications must
rest. lt is generally believed that the mathematical theory of bifurcation requires some
functional analysis and some ofthe methods of topology and dynamics.

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