Moreira's Theorem on the arithmetic sum of dynamically defined Cantor sets

Details Moreira's Theorem on the arithmetic sum of dynamically defined Cantor sets Moreira's Theorem on the arithmetic sum of dynamically defined Cantor sets

2008-07-23

arxiv.org/abs/0807.3709v1

Mathematics

Dynamical Systems

15 pages. Expository notes, will not be submitted

Scientific paper

We present a complete proof of a theorem of C.G. Moreira. Under mild
checkable conditions, the theorem asserts that the Hausdorff dimension of the
arithmetic sum of two dynamically defined Cantor subsets of the real line,
equals either the sum of the dimensions or 1, whichever is smaller.

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