<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>Rectifiable curves in Sierpinski carpets</dc:title>
<dc:creator>Estibalitz Durand-Cartagena</dc:creator><dc:creator>Jeremy Tyson</dc:creator>
<dc:subject>28A80</dc:subject><dc:subject>30L99</dc:subject><dc:subject>11B57</dc:subject><dc:subject>fractal</dc:subject><dc:subject>rectifiable curve</dc:subject><dc:subject>Farey fraction</dc:subject>
<dc:description>We characterize the slopes of nontrivial line segments contained in self-similar and non-self-similar Sierpi\&#39;nski carpets. The set of slopes is related to Farey sequences and the dynamics of punctured square toral billiards. Our results provide a first step towards a description of the rectifiable curves contained in such carpets.</dc:description>
<dc:publisher>Indiana University Mathematics Journal</dc:publisher>
<dc:date>2011</dc:date>
<dc:type>text</dc:type>
<dc:format>pdf</dc:format>
<dc:identifier>10.1512/iumj.2011.60.4382</dc:identifier>
<dc:source>10.1512/iumj.2011.60.4382</dc:source>
<dc:language>en</dc:language>
<dc:relation>Indiana Univ. Math. J. 60 (2011) 285 - 310</dc:relation>
<dc:coverage>state-of-the-art mathematics</dc:coverage>
<dc:rights>http://iumj.org/access/</dc:rights>
</oai_dc:dc>