Chaotic Dynamics for Maps in One and Two Dimensions: a Geometrical Method and Applications to Economics

This article describes a method – called here “the method of Stretching Alongthe Paths” (SAP) – to prove the existence of chaotic sets in discrete-time dy-namical systems. The method of SAP, although mathematically rigorous, isbased on some elementary geometrical considerations and is relatively easy toapply to models arising in applications. The paper provides a description ofthe basic mathematical ideas behind the method, as well as three applicationsto economic models. Incidentally, the paper also discusses some questions con-cerning the definition of chaos and some problems arising from economic modelsin which the dynamics are defined only implicitly.