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Dimension and Measures for a Curvilinear Sierpinski Gasket or Apollonian Packing

✍ Scribed by R.Daniel Mauldin; Mariusz Urbański


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
517 KB
Volume
136
Category
Article
ISSN
0001-8708

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✦ Synopsis


In this paper we apply some results about general conformal iterated function systems to A, the residual set of a standard Apollonian packing or a curvilinear Sierpinski gasket. Within this context, it is straightforward to show that h, the Hausdorff dimension of A, is greater than 1 and the packing dimension and the upper and lower box counting dimensions are all the same as the Hausdorff dimension. Among other things, we verify Sullivan's result that 0<H h (A)< and P h (A)= .