Periodic and Aperiodic Behavior in Discrete Onedimensional Dynamical Systems

摘要

The theory of onedimensional nonlinear difference equations underwent considerable progress in recent years, as the result of the efforts of theorists from several fields - in particular from physics - to get a better understanding, by making use of the notion of the Hopf's bifurcation, of the appearance of cycles and of the transition to aperiodic or chaotic behaviour in physical, biological or ecological systems. These new developments seem to be potentially very useful for the study of periodic and aperiodic phenomena in economics. Parts of this theory have been already used in economic or game theory. The aim of this paper is to present some of these new developments in a compact form which will be, it is hoped, useable by economic theorists. The emphasis will be on the mathematical results of the theory, rather than on its possible applications.