Abstract
Abstract We consider sequences of compositions of quadratic polynomials f c n ( z ) = z 2 + c n . For such sequences one can naturally generalise the definitions of the Julia set and basin of infinity from the autonomous case. In this setting the Julia set depends on a sequence ω = ( c 0 , c 1 , … ) . We study the equilibrium (harmonic) measure on such Julia sets. In particular, we calculate the Hausdorff dimension of the equilibrium measure and study its dependence on the ‘scale of randomnes’.
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