Fixed points imply chaos for a class of multi-valued dynamical systems
by
David R. Stockman
University of Delaware
Coauthors: Brian E. Raines (Baylor University)

We consider multi-valued dynamical systems with continuous time of the form [x\dot] ∈ F(x), where F(x) is a set-valued function. Such models have been studied recently in mathematical economics. We provide a definition for chaos in this type of dynamical system that is in terms of the shift map on the space of all trajectories allowed by the model. By considering this more complicated topological space and its shift map we show that chaos is the `typical' behavior in these models by showing that near any hyperbolic fixed point there is a region where the system is chaotic.

Date received: January 22, 2008