We investigate a family of maps that arises from a model in economics
and game theory. It has some features similar to renormalization and
some similar to intermittency. In a one-parameter family of maps in
dimension 2, when the parameter goes to 0, the maps converge to the
identity. Nevertheless, after a linear rescaling of both space and
time, we get maps with attracting invariant closed curves. As the
parameter goes to 0, those curves converge in a strong sense to a
certain circle. We call those phenomena microdynamics. The model can
be also understood as a family of discrete time approximations to a
Brown-von Neumann differential equation.
Mathematics Subject Classification: 37C70, 37E30.