Moran Sets and Hyperbolic Boundaries

TL;DR

This paper demonstrates that Moran sets are topologically equivalent to hyperbolic boundaries of symbolic spaces and uses this to establish Lipschitz equivalence among certain Moran sets.

Contribution

It generalizes previous results by proving homeomorphism between Moran sets and hyperbolic boundaries, and establishes Lipschitz equivalence for a class of Moran sets.

Findings

Moran sets are homeomorphic to hyperbolic boundaries of symbolic spaces.

Lipschitz equivalence is established for a specific class of Moran sets.

The results extend prior work by Lau and Wang (2009).

Abstract

In the paper, we prove that a Moran set is homeomorphic to the hyperbolic boundary of the representing symbolic space in the sense of Gromov, which generalizes the results of Lau and Wang [Indiana U. Math. J. {\bf 58} (2009), 1777-1795]. Moreover, by making use of this, we establish the Lipschitz equivalence of a class of Moran sets.