Critical exponents and dimension for generalised limit sets

Jonathan M. Fraser; Tianyi Feng

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Critical exponents and dimension for generalised limit sets

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arxiv 2406.19252 v1 pith:XAICQJ4I submitted 2024-06-27 math.MG math.DS

Tianyi Feng , Jonathan M. Fraser This is my paper · ORCID

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keywords limitcriticaldimensionsexponentfractalgeneralisedarbitraryassociated

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There is a beautiful and well-studied relationship between the Poincare exponent and the fractal dimensions of the limit set of a Kleinian group. Motivated by this, given an arbitrary discrete subset of the unit ball we define a critical exponent and investigate how it relates to the fractal dimensions of the associated generalised limit set.

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