Multifractal Structure of Convolution of the Cantor Measure
The multifractal structure of measures generated by iterated function systems (IFS) with overlaps is, to a large extend, unknown. In this paper we study the local dimension of the m-time convolution of the standard Cantor measure μ. By using some combinatoric techniques, we show that the set E of at...
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| Veröffentlicht in: | Advances in applied mathematics 2001-07, Vol.27 (1), p.1-16 |
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| creator | Hu, Tian-You Lau, Ka-Sing |
| description | The multifractal structure of measures generated by iterated function systems (IFS) with overlaps is, to a large extend, unknown. In this paper we study the local dimension of the
m-time convolution of the standard Cantor measure μ. By using some combinatoric techniques, we show that the set
E of attainable local dimensions of μ contains an isolated point. This is rather surprising because when the IFS satisfies the open set condition, the set
E is an interval. The result implies that the multifractal formalism fails without the open set condition. |
| doi_str_mv | 10.1006/aama.2000.0683 |
| format | Article |
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m-time convolution of the standard Cantor measure μ. By using some combinatoric techniques, we show that the set
E of attainable local dimensions of μ contains an isolated point. This is rather surprising because when the IFS satisfies the open set condition, the set
E is an interval. The result implies that the multifractal formalism fails without the open set condition.</description><identifier>ISSN: 0196-8858</identifier><identifier>EISSN: 1090-2074</identifier><identifier>DOI: 10.1006/aama.2000.0683</identifier><identifier>CODEN: AAPMEF</identifier><language>eng</language><publisher>San Diego, CA: Elsevier Inc</publisher><subject>Cantor measure ; convolution ; Exact sciences and technology ; local dimension ; Mathematical analysis ; Mathematical foundations ; Mathematics ; Measure and integration ; multifractal ; multiple representation ; probability ; Probability and statistics ; Probability theory and stochastic processes ; Sciences and techniques of general use</subject><ispartof>Advances in applied mathematics, 2001-07, Vol.27 (1), p.1-16</ispartof><rights>2001 Academic Press</rights><rights>2002 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c356t-2c20fd62d1070b5e54a1c02466330464acf1f5793fe15f91d1c517032500f1723</citedby><cites>FETCH-LOGICAL-c356t-2c20fd62d1070b5e54a1c02466330464acf1f5793fe15f91d1c517032500f1723</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1006/aama.2000.0683$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=14070760$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Hu, Tian-You</creatorcontrib><creatorcontrib>Lau, Ka-Sing</creatorcontrib><title>Multifractal Structure of Convolution of the Cantor Measure</title><title>Advances in applied mathematics</title><description>The multifractal structure of measures generated by iterated function systems (IFS) with overlaps is, to a large extend, unknown. In this paper we study the local dimension of the
m-time convolution of the standard Cantor measure μ. By using some combinatoric techniques, we show that the set
E of attainable local dimensions of μ contains an isolated point. This is rather surprising because when the IFS satisfies the open set condition, the set
E is an interval. The result implies that the multifractal formalism fails without the open set condition.</description><subject>Cantor measure</subject><subject>convolution</subject><subject>Exact sciences and technology</subject><subject>local dimension</subject><subject>Mathematical analysis</subject><subject>Mathematical foundations</subject><subject>Mathematics</subject><subject>Measure and integration</subject><subject>multifractal</subject><subject>multiple representation</subject><subject>probability</subject><subject>Probability and statistics</subject><subject>Probability theory and stochastic processes</subject><subject>Sciences and techniques of general use</subject><issn>0196-8858</issn><issn>1090-2074</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><recordid>eNp1j01LxDAQhoMouK5ePffisXWSNGmLJyl-wS4e1HOI0wQj3WZJUsF_b8oKnjwNA8878z6EXFKoKIC81nqnKwYAFciWH5EVhQ5KBk19TFZAO1m2rWhPyVmMn5nqmOQrcrOdx-Rs0Jj0WLykMGOagym8LXo_fflxTs5Py5o-TNHrKflQbI2OGTonJ1aP0Vz8zjV5u7977R_LzfPDU3-7KZELmUqGDOwg2UChgXdhRK0pAqul5BxqWWu01Iqm49ZQYTs6UBS0Ac4EgKUN42tSHe5i8DEGY9U-uJ0O34qCWtTVoq4WdbWo58DVIbDXEfWY7SZ08S9V5yKNhMy1B87k9l_OBBXRmQnN4ILBpAbv_nvxA9O-ayY</recordid><startdate>20010701</startdate><enddate>20010701</enddate><creator>Hu, Tian-You</creator><creator>Lau, Ka-Sing</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20010701</creationdate><title>Multifractal Structure of Convolution of the Cantor Measure</title><author>Hu, Tian-You ; Lau, Ka-Sing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c356t-2c20fd62d1070b5e54a1c02466330464acf1f5793fe15f91d1c517032500f1723</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Cantor measure</topic><topic>convolution</topic><topic>Exact sciences and technology</topic><topic>local dimension</topic><topic>Mathematical analysis</topic><topic>Mathematical foundations</topic><topic>Mathematics</topic><topic>Measure and integration</topic><topic>multifractal</topic><topic>multiple representation</topic><topic>probability</topic><topic>Probability and statistics</topic><topic>Probability theory and stochastic processes</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hu, Tian-You</creatorcontrib><creatorcontrib>Lau, Ka-Sing</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>Advances in applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hu, Tian-You</au><au>Lau, Ka-Sing</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multifractal Structure of Convolution of the Cantor Measure</atitle><jtitle>Advances in applied mathematics</jtitle><date>2001-07-01</date><risdate>2001</risdate><volume>27</volume><issue>1</issue><spage>1</spage><epage>16</epage><pages>1-16</pages><issn>0196-8858</issn><eissn>1090-2074</eissn><coden>AAPMEF</coden><abstract>The multifractal structure of measures generated by iterated function systems (IFS) with overlaps is, to a large extend, unknown. In this paper we study the local dimension of the
m-time convolution of the standard Cantor measure μ. By using some combinatoric techniques, we show that the set
E of attainable local dimensions of μ contains an isolated point. This is rather surprising because when the IFS satisfies the open set condition, the set
E is an interval. The result implies that the multifractal formalism fails without the open set condition.</abstract><cop>San Diego, CA</cop><pub>Elsevier Inc</pub><doi>10.1006/aama.2000.0683</doi><tpages>16</tpages><oa>free_for_read</oa></addata></record> |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Cantor measure convolution Exact sciences and technology local dimension Mathematical analysis Mathematical foundations Mathematics Measure and integration multifractal multiple representation probability Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use |
| title | Multifractal Structure of Convolution of the Cantor Measure |
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