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: