``What really happens when a smooth expanding map is iterated on
the computer''
February 25, 1999
Smooth expanding maps tend to have very strong ergodicity properties,
and these properties can be "observed experimentally" by iterating the
map on the computer. What is actually iterated on the computer is,
however, not the smooth map itself, but rather a discretization of
it
-- quite a different kind of mathematical object. It is a fact of
experience that iteration of the discretized map usually -- but not
always -- mimics remarkably well iteration of the original smooth
map. I believe that we do not have anything approaching a satisfactory
explanation for this fact. In the talk, I will discuss what I think
needs to be shown, make a number of general observations situating the
problem, and describe some preliminary results.