Iterated function systems, Ruelle operators, and invariant projective measures

Details Iterated function systems, Ruelle operators, and invariant projective measures Iterated function systems, Ruelle operators, and invariant projective measures

2005-01-06

arxiv.org/abs/math/0501077v3

Math. Comp. 75 (2006), 1931--1970

Mathematics

Dynamical Systems

39 pages, LaTeX "amsart" class. v2, a little clarification added. v3: new introductory section, pages 2-4; explanation of nota

Scientific paper

We introduce an harmonic analysis for iterated function systems (IFS) (X, mu) which is based on a Markov process on certain paths. The probabilities are determined by a weight function W on X. From W we define a transition operator R_W acting on functions on X, and a corresponding class of R_W-harmonic functions. The properties of these functions determine the spectral theory of L^2(mu). For affine IFSs we establish orthogonal bases in L^2(mu). These bases are generated by paths with infinite repetition of finite words. We use this in the last section to analyze tiles in R^d.

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