Parabolic iterated function systems with overlaps
by
Boris Solomyak
University of Washington
Coauthors: Károly Simon, Mariusz Urbanski

The well-known Bowen-Ruelle pressure formula provides the dimension of the attractor for a hyperbolic iterated function system (i.f.s.) when the are no överlaps" (that is, the open set condition is satisfied). Urbanski extended this approach to parabolic i.f.s. without overlaps. On the other hand, K. Simon and the speaker have shown that the pressure formula "typically" holds even when there are overlaps, assuming that the contractions are sufficiently ßtrong." As we show, results of this kind can be obtained even for some parabolic i.f.s. with overlaps, provided that the parabolic point is not in the överlapping region." The main example that we consider arises from a class of continued fractions.

Date received: February 24, 1998