  In rational dynamics, we prove the existence of a polynomial that satisfies
the Topological Collet-Eckmann condition, but which has a recurrent critical
orbit that is not Collet-Eckmann. This shows that the converse of the main
theorem in [11] does not hold.
  In interval dynamics, we show that the Collet-Eckmann property for recurrent
critical orbits is not a topological invariant for real polynomials with
negative Schwarzian derivative. This contradicts a conjecture of Swiatek [22].
