NEW RESULTS ON MEASURES OF MAXIMAL ENTROPY

It has recently been demonstrated that there are strongly irreducible subshifts of finite type with more than one measure of maximal entropy . Here we obtain a number of results concerning the uniqueness of the measure of maximal entropy. In addition, we construct for any d greate r than or equal to 2 and k a strongly irreducible subshift of finite t ype in d dimensions with exactly k ergodic (extremal) measures of maxi mal entropy. For d greater than or equal to 3, we construct a strongly irreducible subshift of finite type in d dimensions with a continuum of ergodic measures of maximal entropy.