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On Hausdorff dimension and cusp excursions for Fuchsian groups

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  • Certain subsets of limit sets of geometrically finite Fuchsian groups with parabolic elements are considered. It is known that Jarník limit sets determine a "weak multifractal spectrum" of the Patterson measure in this situation. This paper will describe a natural generalisation of these sets, called strict Jarník limit sets, and show how these give rise to another weak multifractal spectrum. Number-theoretical interpretations of these results in terms of continued fractions will also be given.
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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