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Deterministic and random aspects of porosities

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  • 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.
    Mathematics Subject Classification: 28A12, 28A80.

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