On Poincaré Series of Unicritical Polynomials at the Critical Point

Abstract

In this paper, we show that for a unicritical polynomial having a priori bounds, the unique conformal measure of minimal exponent has no atom at the critical point. For a conformal measure of higher exponent, we give a necessary and sufficient condition for the critical point to be an atom, in terms of the growth rate of the derivatives at the critical value.

Keywords

Complex dynamics / Julia sets / Poincaré series / Summability condition

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