Computability in Europe 2008
Logic and Theory of Algorithms

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Regular Talk:
Comparing Notions of Fractal Dimension

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Speaker: Chris J. Conidis
Author(s): Chris J. Conidis
Slot: Wed, 16:50-17:10, Room 24 (col. 3)

Abstract

We examine the relationship between classical packing dimension and effective packing dimension. In particular, we construct $\Pi^0_1$-class $X$ that has classical packing dimension 0 and effective packing dimension 1. This answers a question of Lutz, who asked if there is a correspondence principle for packing dimension, as in the case for Hausdorff dimension. We also examine the relationship between upper box dimension and effective packing dimension on the set of $\Pi^0_1$-classes.


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