ABSTRACT
Thia is, of course, not new: in fact, here, with the hyperbolicity poeaeased by
elementary proof), and the dynamics on Q• are those of the one-aided shift on
two symbols. However, for our conclUiion the hyperbolicity present in this map is
not necessary. (Weakening the assumptions also means that the largest invariant
and the unique expander contains both symbol sets. Aa before, the symbol sets
are also the pre-expandera, that is, P1 = En81 with I(P1) = E = [-1, 1] E £and
P2 =En 82 with I(P2) = E = [-1, 1] E £. Hence, applying the Chaos Lemma,
we have a stronger lemma: