$C^m$ Eigenfunctions of Perron-Frobenius Operators and a New Approach to Numerical Computation of Hausdorff Dimension: Applications in ${\mathbb{R}}^1$

Richard S. Falk, Roger D. Nussbaum

We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case that we consider her…