Infinite Non-Conformal Iterated Function Systems

Abstract

We consider a generalisation of the self-affine iterated function systems of Lalley and Gatzouras by allowing for a countable infinity of non-conformal contractions. It is shown that the Hausdorff dimension of the limit set is equal to the supremum of the dimensions of compactly supported ergodic measures. In addition we consider the multifractal analysis for countable families of potentials. We obtain a conditional variational principle for the level sets.

37 pages

References in corpus (3)

• The thermodynamic approach to multifractal analysis
• Weighted thermodynamic formalism and applications
• Regularity of multifractal spectra of conformal iterated function systems