A piecewise contraction is defined on a finite partition of
a metric phase space (X,d). Each partition element is mapped
by a contraction into X. Since the contraction is only piecewise,
it is not a priori clear (and true) that orbits are attracted
to periodic orbits. However, in joint work with Jonathan Deane
(University of Surrey), we prove that for parametrized families
of planar piecewise contractions, typically all orbits are
asymptotically periodic. The method can be extended to higher
dimension and systems with varying partitions as well. |