Computing Hausdorff Dimension of Invariant Measure of Circle Maps

Among the dimensional characteristics, Hausdorff dimension is an important one. Hausdorff dimensions of the invariant measure of circle homeomorphisms are well studied for unbounded type rotation numbers. In this work, we calculated the Hausdorff dimension for bounded type rotation numbers. Keywords: piecewise linear circle maps, invariant measure, Hausdorff dimension, pointwise dimensions, iteration.