Overlap numbers for measures in conformal iterated systems
I will present new notions of overlap numbers for projections of equilibrium measures in conformal iterated function systems without Open Set Condition. The presence of overlaps complicates matters significantly, and the behavior of such systems is very different from the systems with separation conditions. We will associate a lift endomorphism, and show that the overlap numbers are related to the notion of folding entropy of invariant measures introduced by Ruelle. We will give estimates on the Hausdorff dimensions of projections
of equilibrium measures by using pressure functions and overlap numbers. We will also discuss certain examples of conformal iterated function systems with overlaps.
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