99-22 J. Schmeling and S. Troubetzkoy

Entropy regular sets (60K, dvi file) Jan 21, 99

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Abstract. One of the objects of geometric measure theory is to derive global geometric structures from local properties (densities with respect to the $s$--dimensional Hausdorff measure). In the framework of dynamical system it is more natural to consider entropy measures instead of Hausdorff measures. Our aim is to show that {\em regular} subshifts (with respect to the entropy measure) necessarily have a special rigid structure. Moreover, their entropy has to be the logarithm of an integer. This parallels the well known fact that regular sets (with respect to the Hausdorff measure) have to have integral dimension.

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