Normal Forms, Bifurcations and Finiteness Problems in Differential Equations

A number of recent significant developments in the theory of differential equations are presented in an elementary fashion, many of which are scattered throughout the literature and have not previously appeared in book form, the common denominator being the theory of planar vector fields (real or complex). A second common feature is the study of bifurcations of dynamical systems. Moreover, the book links fields that have developed independently and signposts problems that are likely to become significant in the future. The following subjects are covered: new tools for local and global properties of systems and families of systems, nonlocal bifurcations, finiteness properties of Pfaffian functions and of differential equations, geometric interpretation of the Stokes phenomena, analytic theory of ordinary differential equations and complex foliations, applications to Hilbert's 16th problem. Readership: Graduate students, postdocs and researchers in dynamical systems with a minimum background of a one-year course on nonlinear differential equations. 'Skeletal metastases are both a common and devastating consequence of a spectrum of cancers.Significant advances have occurred in our understanding of the pathobiology of this process. This text provides a comprehensive review of current investigative findings and their clinical implications.' Steven T. Rosen, M.D. Series Editor