Symmetries of Julia sets in higher dimensions
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Conformal internal symmetry of 2d σ-models coupled to gravity and a dilaton
General Relativity reduced to two dimensions possesses a large group of symmetries that exchange classical solutions. The associated Lie algebra is known to contain the affine Kac-Moody algebra A (1) 1 and half of a real Witt algebra. In this paper we exhibit the full symmetry under the semi-direct product of Lie(A (1) 1 ) by the Witt algebra Lie(W). Furthermore we exhibit the corresponding hid...
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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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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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