Wiggly sets and limit sets

Christopher J. Bishop Mathematics Department, State University of New York at Stony Brook Peter W. Jones Mathematics Department, Yale University

TBD mathscidoc:1701.332871

Arkiv for Matematik, 35, (2), 201-224, 1996.1
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.
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  title={Wiggly sets and limit sets},
  author={Christopher J. Bishop, and Peter W. Jones},
  booktitle={Arkiv for Matematik},
Christopher J. Bishop, and Peter W. Jones. Wiggly sets and limit sets. 1996. Vol. 35. In Arkiv for Matematik. pp.201-224. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203550462601680.
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