On Finite Blaschke Products whose Restrictions to the unit circle are Exact Endomorphisms

An easily checked sufficient condition is given for the restrictionof a finite Blaschke product to the unit circle to be an exactendomorphism. A formula for the entropy of such restrictionswith respect to the unique finite invariant measure equivalentto Lebesgue measure is given and it is shown that if such arestriction has maximal entropy then it is conformally equivalentto the product of a rotation and a power.