January  2002, 8(1): 121-136. doi: 10.3934/dcds.2002.8.121

Deterministic and random aspects of porosities

1. 

Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FIN-40351 Jyväskylä, Finland, Finland

2. 

Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430, United States

Received  June 2000 Revised  September 2001 Published  October 2001

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.
Citation: Esa Järvenpää, Maarit Järvenpää, R. Daniel Mauldin. Deterministic and random aspects of porosities. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 121-136. doi: 10.3934/dcds.2002.8.121
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