Deterministic and random aspects of porosities

Esa Järvenpää; Maarit Järvenpää; R. Daniel Mauldin

doi:10.3934/dcds.2002.8.121

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2002, Volume 8, Issue 1: 121-136. Doi: 10.3934/dcds.2002.8.121

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Deterministic and random aspects of porosities

1.
Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FIN-40351 Jyväskylä
2.
Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430

Received: May 31, 2000

Revised: August 31, 2001

Published: December 2001

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Abstract

We study porosities of limit sets of finite conformal iterated function systems and certain random fractals. We characterize systems with positive porosity and prove that porosity is continuous within a special class of one dimensional systems. We also show that for certain typical random recursive constructions related to fractal percolation both 0-porous and 1/2-porous points are dense, that is, porosity obtains its minimum and maximum values in a dense set.

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Mathematics Subject Classification: 28A12, 28A80.

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