Abstract
We show that a compact, connected set which has uniform oscillations at all points and at all scales has dimension strictly larger than 1. We also show that limit sets of certain Kleinian groups have this property. More generally, we show that if G is a non-elementary, analytically finite Kleinian group, and its limit set Λ(G) is connected, then Λ(G) is either a circle or has dimension strictly bigger than 1.
Funding Statement
The first author is partially supported by NSF Grant DMS 95-00577 and an Alfred P. Sloan research fellowship. The second author is partially supported by NSF grant DMS-94-23746.
Citation
Christopher J. Bishop. Peter W. Jones. "Wiggly sets and limit sets." Ark. Mat. 35 (2) 201 - 224, October 1997. https://doi.org/10.1007/BF02559967
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