<oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:title>Self-similar sets as hyperbolic boundaries</dc:title>
<dc:creator>Ka-Sing Lau</dc:creator><dc:creator>Xiang-Yang Wang</dc:creator>
<dc:subject>28A78</dc:subject><dc:subject>28A80</dc:subject><dc:subject>boundary</dc:subject><dc:subject>geodesic ray</dc:subject><dc:subject>hyperbolic graph</dc:subject><dc:subject>iterated function system</dc:subject><dc:subject>self-similar sets</dc:subject><dc:subject>open set condition</dc:subject>
<dc:description>We show that, for an iterated function system $\{S_j\}_{j=1}^N$ of similitudes that satisfies the open set condition, there is a natural graph structure in the representing symbolic space to make it a hyperbolic graph, and the hyperbolic boundary is homeomorphic to the self-similar set generated by $\{S_j\}_{j=1}^N$.</dc:description>
<dc:publisher>Indiana University Mathematics Journal</dc:publisher>
<dc:date>2009</dc:date>
<dc:type>text</dc:type>
<dc:format>pdf</dc:format>
<dc:identifier>10.1512/iumj.2009.58.3639</dc:identifier>
<dc:source>10.1512/iumj.2009.58.3639</dc:source>
<dc:language>en</dc:language>
<dc:relation>Indiana Univ. Math. J. 58 (2009) 1777 - 1796</dc:relation>
<dc:coverage>state-of-the-art mathematics</dc:coverage>
<dc:rights>http://iumj.org/access/</dc:rights>
</oai_dc:dc>