Moreira's Theorem on the arithmetic sum of dynamically defined Cantor sets
Dynamical Systems
2008-07-24 v1 Classical Analysis and ODEs
Abstract
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.
Keywords
Cite
@article{arxiv.0807.3709,
title = {Moreira's Theorem on the arithmetic sum of dynamically defined Cantor sets},
author = {Pablo Shmerkin},
journal= {arXiv preprint arXiv:0807.3709},
year = {2008}
}
Comments
15 pages. Expository notes, will not be submitted