In some applications it is convinient to have a representation
of a given system in which periodic points are absent. The
natural way to this is by creating a topological extension which is 1-1
on the
supports of all aperiodic ergodic measures and splits only the periodic
points (into nonperiodic points). Further, it is desirable that the
periodic orbits, after splitting, do not support any entropy. I will
present a (fairly
complicated) method of achieving such an extension, assuming that the
system is zero-dimensional or has the small boundary property.
This is part of a joint work in progress with
David Burguet from CNRS.