Hierarchy of graph matchbox manifolds

Details Hierarchy of graph matchbox manifolds Hierarchy of graph matchbox manifolds

2011-07-26

arxiv.org/abs/1107.5303v2

Mathematics

Dynamical Systems

A new result added; a few references added; exposition improved

Scientific paper

We study a class of graph foliated spaces, or graph matchbox manifolds, initially constructed by Kenyon and Ghys. For graph foliated spaces we introduce a quantifier of dynamical complexity which we call a level. We develop the \emph{fusion} construction, which allows us to associate to every two graph foliated spaces a third one which contains the former two in its closure. Although the underlying idea of the fusion is very simple, it gives us a powerful tool to study graph foliated spaces. Using fusion, we prove that there is a hierarchy of graph foliated spaces at infinite levels. We also construct examples of graph foliated spaces with various dynamical and geometric properties.

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