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  <doc>
    <id>119</id>
    <completedYear>2009</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2010-02-10</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hausdorff measure of uniform self-similar fractals</title>
    <abstract language="eng">Let &lt;i&gt;d&lt;/i&gt; &amp;#8805; 1 be an integer and &lt;i&gt;E&lt;/i&gt; a self-similar fractal set, which is the attractor of a uniform contracting iterated function system (UIFS) on R&lt;sup&gt;d&lt;/sup&gt;. Denote by &lt;i&gt;D&lt;/i&gt; the Hausdorff dimension, by &lt;i&gt;H&lt;/i&gt;&lt;sup&gt;D&lt;/sup&gt;&lt;i&gt;(E)&lt;/i&gt; the Hausdorff measure and by diam &lt;i&gt;(E)&lt;/i&gt; the diameter of &lt;i&gt;E&lt;/i&gt;. If the UIFS is parametrised by its contracting factor &lt;i&gt;c&lt;/i&gt;, while the set &amp;omega; of fixed points of the UIFS does not depend on &lt;i&gt;c&lt;/i&gt;, we will show the existence of a positive constant depending only on &amp;omega;, such that the Hausdorff dimension is smaller than one and &lt;i&gt;H&lt;/i&gt;&lt;sup&gt;D&lt;/sup&gt; = &lt;i&gt;(E)&lt;/i&gt; &lt;sup&gt;D&lt;/sup&gt; if &lt;i&gt;c&lt;/i&gt; is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover we present a parametrised UIFS where &amp;omega; depends on &lt;i&gt;c&lt;/i&gt; and &lt;i&gt;H&lt;/i&gt;&lt;sup&gt;D&lt;/sup&gt; &lt; diam&lt;i&gt;(E)&lt;/i&gt;&lt;sup&gt;D&lt;/sup&gt;, if &lt;i&gt;c&lt;/i&gt; is small enough.</abstract>
    <identifier type="urn">urn:nbn:de:bvb:739-opus-17948</identifier>
    <identifier type="opus3-id">1794</identifier>
    <note>This is a preprint of an article accepted for publication in Analysis in Theory and Applications ISSN: 1672-4070 (print version) ISSN: 1573-8175 (electronic version) Copyright (c) by Springer. The original publication is available at www.springerlink.com</note>
    <enrichment key="SourceTitle">Analysis in Theory and Applications ISSN: 1672-4070 (print version) ISSN: 1573-8175 (electronic version)</enrichment>
    <licence>Standardbedingung laut Einverständniserklärung</licence>
    <author>Wolfgang Kreitmeier</author>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Maßtheorie</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Iteriertes Funktionensystem</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Hausdorff-Dimension</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Hausdorff-Maß</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Self-similar set</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Hausdorff measure</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="28A78">Hausdorff and packing measures</collection>
    <collection role="msc" number="28A80">Fractals [See also 37Fxx]</collection>
    <collection role="open_access" number="">open_access</collection>
    <collection role="institutes" number="">Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik</collection>
    <thesisPublisher>Universität Passau</thesisPublisher>
    <file>https://opus4.kobv.de/opus4-uni-passau/files/119/haus_meas_v3.pdf</file>
  </doc>
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