Karma Dajani,
Martijn de Vries
(2007)
Let be a non-integer. We consider expansions of the form , where the
digits are generated by means of a Borel map defined on . We show existence and uniqueness of a -invariant probability measure, absolutely continuous with respect to , where is the Bernoulli measure on with parameter () and is the normalized Lebesgue measure on . Furthermore, this measure is of the form , where is equivalent to . We prove that the measure of maximal entropy and are mutually...