Higher Multifractal Analysis for Simultaneous Actions of Fuchsian Groups

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We consider groups Γ1, Γ2, …, Γ d acting on the hyperbolic plane H 2 and by the method of Series for coding hyperbolic geodesics we can do simultaneous multifractal decompositions from the action of these groups. We obtain a variational formula for a dimension of the multifractal sets which generalizes that presented in our previous article for d = 1.