The Fatou-Sullivan Dictionary
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(A lot of this table/post was written quickly and needs reorganization/explanation/citations.)
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(A lot of this table/post was written quickly and needs reorganization/explanation/citations.)
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I want to do some posts on my favorite topological space, the Cantor set. Cantor sets serve as important examples in virtually all fields of anlaysis and dynamical systems, as well as in geometric group theory and foliation theory. In this post I will describe some basic topological properties of Cantor sets, and in a following post I will describe some group actions on cantor sets.
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(A lot of this table/post was written quickly and needs reorganization/explanation/citations.)
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I want to do some posts on my favorite topological space, the Cantor set. Cantor sets serve as important examples in virtually all fields of anlaysis and dynamical systems, as well as in geometric group theory and foliation theory. In this post I will describe some basic topological properties of Cantor sets, and in a following post I will describe some group actions on cantor sets.
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Note: This post first appeared on a now defunct blog on January 19, 2019
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Problem: Show that for almost every $x>1$ that {$x^k\mod 1$} is dense in $[0,1]$.
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Note: This post first appeared on a now defunct blog on January 19, 2019
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I want to do some posts on my favorite topological space, the Cantor set. Cantor sets serve as important examples in virtually all fields of anlaysis and dynamical systems, as well as in geometric group theory and foliation theory. In this post I will describe some basic topological properties of Cantor sets, and in a following post I will describe some group actions on cantor sets.
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