Large intersection classes on fractals

Mathematics – Dynamical Systems

Scientific paper

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Scientific paper

We consider limit sets of some conformal iterated function systems, and
introduce classes of subsets of the limit set, with the property that the
classes are closed under countable intersections and all sets in the classes
have large Hausdorff dimension. We show some applications in ergodic theory,
Diophantine approximation and complex dynamics.

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