Sumi, Hiroki

Dimensions of Julia sets of expanding rational semigroups


We estimate the upper box and Hausdorff dimensions of the Julia set of an expanding semigroup generated by finitely many rational functions, using the thermodynamic formalism in ergodic theory. Furthermore, we show the existence and uniqueness of a conformal measure, for a finitely generated expanding semigroup satisfying the open set condition.

submission: 19 January, 2004
revision: 27 May, 2004
revision: 28 September, 2004
revision: 9 April, 2005
revision: 3 June, 2005
revision: 29 June, 2005
to appear in Kodai Math. J.

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