2 3 Se p 20 05 Dimensions of Julia sets of expanding rational semigroups ∗

نویسنده

  • Hiroki Sumi
چکیده

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 Bowen’s formula, and the existence and uniqueness of a conformal measure, for a finitely generated expanding semigroup satisfying the open set condition.

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Se p 20 05 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 Bowen’s formula, and the existence and uniqueness of a conformal measure, for a finitely generated expanding semigroup satisfying the open set condition.

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تاریخ انتشار 2008