Nonlinear dynamical economics and chaotic motion (Q1801288)

This is a useful monograph which presents the essential ideas of nonlinear dynamics with examples drawn from several fields of economic theory, not only business cycle theory. The introductory chapter discusses the roots of deterministic mechanical thinking. Further chapters include a presentation of the Poincaré-Bendixson-theorem and limit cycles with various applications. After a section on bifurcations, there follows an extensive account of chaotic dynamics in discrete and continuous time. A special chapter deals with numerical tools and tests to identify chaotic dynamics in time series. There is also a chapter on catastrophe theory. The exposition assembles theorems, usually without proof but with references to the sources where proofs can be found. The book is well readable, considering the difficulty of the subject.