  A conservative irrational pseudo-rotation of the two-torus is semi-conjugate
to the irrational rotation if and only if it has the property of bounded mean
motion [10]. (Here 'irrational pseudo-rotation' means a toral homeomorphism
with uniquely defined, totally irrational rotation vector.) The aim of this
note is to explore this concept some further. For instance, we provide an
example which shows that the preceding statement does not hold in the
non-conservative case. Further, we collect a number of observations concerning
the case where the bounded mean motion property fails. In particular, we show
that a non-wandering irrational pseudo-rotation of the two-torus with unbounded
mean motion has sensitive dependence on initial conditions.
