Abstract:Granville recently asked how the Mahler measure behaves in the context of polynomial dynamics. For a polynomial π (π§) = π§ π + . . . β C[π§ ], deg( π ) β₯ 2, we show that the Mahler measure of the iterates π π grows geometrically fast with the degree π π , and find the exact base of that exponential growth. This base is expressed via an integral of log + | π§ | with respect to the invariant measure of the Julia set for the polynomial π . Moreover, we give sharp estimates for such an integral when the J… Show more
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