A Characterization of Hyperbolic Affine Iterated Function Systems
نویسندگان
چکیده
The two main theorems of this paper provide a characterization of hyperbolic affine iterated function systems defined on R. Atsushi Kameyama [Distances on topological self-similar sets, in Fractal Geometry and Applications: A Jubilee of Benǒit Mandelbrot. Proceedings of Symposia in Pure Mathematics, Volume 72, Part 1, 2004, pages 117–129] asked the following fundamental question: Given a topological self-similar set, does there exist an associated system of contraction mappings? Our theorems imply an affirmative answer to Kameyama’s question for self-similar sets derived from affine transformations on R.
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