Hausdorff dimension and measure of basin boundaries (Q1263144)

In this paper the author first gives a short survey of the Metropolis, Stein, and Stein theory of unimodal maps and maximal shift sequences. Then he uses this MSS theory to analyze a piecewise linear map with a super stable periodic point of period 3. He introduces the concept of graph directed constructions and develops an according algorithm for obtaining the boundary of the basin of attraction for the above stable orbit. In the third part of the paper the Hausdorff dimension of that boundary is calculated and its measure is shown to be finite and positive. Some problems that might arise when trying to generalize the outlined approach are explained.