Analyticity of Hausdorff dimension of limit sets of Kleinian groups.

Anderson, James W.; Rocha, André C.

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Displaying similar documents to “Analyticity of Hausdorff dimension of limit sets of Kleinian groups.”

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We investigate the properties of the Hausdorff dimension of the attractor of the iterated function system (IFS) {γx,λx,λx+1}. Since two maps have the same fixed point, there are very complicated overlaps, and it is not possible to directly apply known techniques. We give a formula for the Hausdorff dimension of the attractor for Lebesgue almost all parameters (γ,λ), γ < λ. This result only holds for almost all parameters: we find a dense set of parameters (γ,λ) for which the Hausdorff...