# [FOM] Category and Measure

John McCarthy jmc at cs.stanford.edu
Mon Sep 17 20:13:24 EDT 2007

Sorry.  I misremembered what I had proved.

Let x to F(x) + \lambda be transformations of the unit circle into
itself.  The "typical" behavior is that for each rational number  q, there
is an interval of values of \lambda for which the Poincare rotation
number of the transformation is q.  For a suitable metric, max
difference I suppose, on the space of Fs, the set of Fs for which the
behavior is typical, is of second category.