Dimension of Besicovitch–Eggleston sets in countable symbolic space
This paper is mainly concerned with Hausdorff dimensions of Besicovitch--Eggleston subsets in countable symbolic space. A notable point is that the dimension values possess a universal lower bound depending only on the underlying metric. As a consequence of the main results, we obtain Hausdorff dime...
Gespeichert in:
| Veröffentlicht in: | Nonlinearity 2010-05, Vol.23 (5), p.1185-1197 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1197 |
|---|---|
| container_issue | 5 |
| container_start_page | 1185 |
| container_title | Nonlinearity |
| container_volume | 23 |
| creator | Fan, Aihua Liao, Lingmin Ma, Jihua Wang, Baowei |
| description | This paper is mainly concerned with Hausdorff dimensions of Besicovitch--Eggleston subsets in countable symbolic space. A notable point is that the dimension values possess a universal lower bound depending only on the underlying metric. As a consequence of the main results, we obtain Hausdorff dimension formulae for sets of real numbers with prescribed digit frequencies in their Luroth expansions. |
| doi_str_mv | 10.1088/0951-7715/23/5/009 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_pasca</sourceid><recordid>TN_cdi_pascalfrancis_primary_22769670</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1671236650</sourcerecordid><originalsourceid>FETCH-LOGICAL-c416t-a68373659c28205684a437a9e1cfff49d6f7c6403763175d06dd98c3800b36543</originalsourceid><addsrcrecordid>eNqNkLFOwzAURS0EEqXwA0xZkOgQ-mzHdjwWKBSpEgvMluvY1CiNQ5xW6sY_8Id8CYmCurAwWXo-9zy9i9AlhhsMeT4FyXAqBGZTQqdsCiCP0AhTjlPOsuwYjQ7AKTqL8R0A45zQEZrf-42tog9VElxya6M3Yedbs_7-_Jq_vZU2tt1XtG1MfJWYsK1avSptEvebVSi9SWKtjT1HJ06X0V78vmP0-jB_uVuky-fHp7vZMjUZ5m2qeU4F5UwakhNgPM90RoWWFhvnXCYL7oThGVDBKRasAF4UMjc0B1h1sYyO0WTwrnWp6sZvdLNXQXu1mC1VPwPgkgKhO9yx1wNbN-Fj292hNj4aW5a6smEbFeYCE8o5gw4lA2qaEGNj3cGNQfX9qr4-1denCFWsWyO70NWvX0ejS9foyvh4SBIiuOSil6cD50P9P-_kL_-XU3Xh6A8DGZNc</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1671236650</pqid></control><display><type>article</type><title>Dimension of Besicovitch–Eggleston sets in countable symbolic space</title><source>IOP Publishing Journals</source><source>Institute of Physics (IOP) Journals - HEAL-Link</source><creator>Fan, Aihua ; Liao, Lingmin ; Ma, Jihua ; Wang, Baowei</creator><creatorcontrib>Fan, Aihua ; Liao, Lingmin ; Ma, Jihua ; Wang, Baowei</creatorcontrib><description>This paper is mainly concerned with Hausdorff dimensions of Besicovitch--Eggleston subsets in countable symbolic space. A notable point is that the dimension values possess a universal lower bound depending only on the underlying metric. As a consequence of the main results, we obtain Hausdorff dimension formulae for sets of real numbers with prescribed digit frequencies in their Luroth expansions.</description><identifier>ISSN: 0951-7715</identifier><identifier>EISSN: 1361-6544</identifier><identifier>DOI: 10.1088/0951-7715/23/5/009</identifier><language>eng</language><publisher>Bristol: IOP Publishing</publisher><subject>Digits ; Exact sciences and technology ; Global analysis, analysis on manifolds ; Lower bounds ; Mathematical methods in physics ; Mathematics ; Nonlinearity ; Other topics in mathematical methods in physics ; Physics ; Real numbers ; Sciences and techniques of general use ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><ispartof>Nonlinearity, 2010-05, Vol.23 (5), p.1185-1197</ispartof><rights>2015 INIST-CNRS</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c416t-a68373659c28205684a437a9e1cfff49d6f7c6403763175d06dd98c3800b36543</citedby><cites>FETCH-LOGICAL-c416t-a68373659c28205684a437a9e1cfff49d6f7c6403763175d06dd98c3800b36543</cites><orcidid>0000-0001-6723-1362</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://iopscience.iop.org/article/10.1088/0951-7715/23/5/009/pdf$$EPDF$$P50$$Giop$$H</linktopdf><link.rule.ids>230,314,776,780,881,27903,27904,53809,53889</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22769670$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-00693023$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Fan, Aihua</creatorcontrib><creatorcontrib>Liao, Lingmin</creatorcontrib><creatorcontrib>Ma, Jihua</creatorcontrib><creatorcontrib>Wang, Baowei</creatorcontrib><title>Dimension of Besicovitch–Eggleston sets in countable symbolic space</title><title>Nonlinearity</title><description>This paper is mainly concerned with Hausdorff dimensions of Besicovitch--Eggleston subsets in countable symbolic space. A notable point is that the dimension values possess a universal lower bound depending only on the underlying metric. As a consequence of the main results, we obtain Hausdorff dimension formulae for sets of real numbers with prescribed digit frequencies in their Luroth expansions.</description><subject>Digits</subject><subject>Exact sciences and technology</subject><subject>Global analysis, analysis on manifolds</subject><subject>Lower bounds</subject><subject>Mathematical methods in physics</subject><subject>Mathematics</subject><subject>Nonlinearity</subject><subject>Other topics in mathematical methods in physics</subject><subject>Physics</subject><subject>Real numbers</subject><subject>Sciences and techniques of general use</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><issn>0951-7715</issn><issn>1361-6544</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNqNkLFOwzAURS0EEqXwA0xZkOgQ-mzHdjwWKBSpEgvMluvY1CiNQ5xW6sY_8Id8CYmCurAwWXo-9zy9i9AlhhsMeT4FyXAqBGZTQqdsCiCP0AhTjlPOsuwYjQ7AKTqL8R0A45zQEZrf-42tog9VElxya6M3Yedbs_7-_Jq_vZU2tt1XtG1MfJWYsK1avSptEvebVSi9SWKtjT1HJ06X0V78vmP0-jB_uVuky-fHp7vZMjUZ5m2qeU4F5UwakhNgPM90RoWWFhvnXCYL7oThGVDBKRasAF4UMjc0B1h1sYyO0WTwrnWp6sZvdLNXQXu1mC1VPwPgkgKhO9yx1wNbN-Fj292hNj4aW5a6smEbFeYCE8o5gw4lA2qaEGNj3cGNQfX9qr4-1denCFWsWyO70NWvX0ejS9foyvh4SBIiuOSil6cD50P9P-_kL_-XU3Xh6A8DGZNc</recordid><startdate>20100501</startdate><enddate>20100501</enddate><creator>Fan, Aihua</creator><creator>Liao, Lingmin</creator><creator>Ma, Jihua</creator><creator>Wang, Baowei</creator><general>IOP Publishing</general><general>Institute of Physics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>L7M</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0001-6723-1362</orcidid></search><sort><creationdate>20100501</creationdate><title>Dimension of Besicovitch–Eggleston sets in countable symbolic space</title><author>Fan, Aihua ; Liao, Lingmin ; Ma, Jihua ; Wang, Baowei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c416t-a68373659c28205684a437a9e1cfff49d6f7c6403763175d06dd98c3800b36543</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Digits</topic><topic>Exact sciences and technology</topic><topic>Global analysis, analysis on manifolds</topic><topic>Lower bounds</topic><topic>Mathematical methods in physics</topic><topic>Mathematics</topic><topic>Nonlinearity</topic><topic>Other topics in mathematical methods in physics</topic><topic>Physics</topic><topic>Real numbers</topic><topic>Sciences and techniques of general use</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fan, Aihua</creatorcontrib><creatorcontrib>Liao, Lingmin</creatorcontrib><creatorcontrib>Ma, Jihua</creatorcontrib><creatorcontrib>Wang, Baowei</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Nonlinearity</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fan, Aihua</au><au>Liao, Lingmin</au><au>Ma, Jihua</au><au>Wang, Baowei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dimension of Besicovitch–Eggleston sets in countable symbolic space</atitle><jtitle>Nonlinearity</jtitle><date>2010-05-01</date><risdate>2010</risdate><volume>23</volume><issue>5</issue><spage>1185</spage><epage>1197</epage><pages>1185-1197</pages><issn>0951-7715</issn><eissn>1361-6544</eissn><abstract>This paper is mainly concerned with Hausdorff dimensions of Besicovitch--Eggleston subsets in countable symbolic space. A notable point is that the dimension values possess a universal lower bound depending only on the underlying metric. As a consequence of the main results, we obtain Hausdorff dimension formulae for sets of real numbers with prescribed digit frequencies in their Luroth expansions.</abstract><cop>Bristol</cop><pub>IOP Publishing</pub><doi>10.1088/0951-7715/23/5/009</doi><tpages>13</tpages><orcidid>https://orcid.org/0000-0001-6723-1362</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0951-7715 |
| ispartof | Nonlinearity, 2010-05, Vol.23 (5), p.1185-1197 |
| issn | 0951-7715 1361-6544 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_22769670 |
| source | IOP Publishing Journals; Institute of Physics (IOP) Journals - HEAL-Link |
| subjects | Digits Exact sciences and technology Global analysis, analysis on manifolds Lower bounds Mathematical methods in physics Mathematics Nonlinearity Other topics in mathematical methods in physics Physics Real numbers Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Dimension of Besicovitch–Eggleston sets in countable symbolic space |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-21T14%3A10%3A04IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_pasca&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Dimension%20of%20Besicovitch%E2%80%93Eggleston%20sets%20in%20countable%20symbolic%20space&rft.jtitle=Nonlinearity&rft.au=Fan,%20Aihua&rft.date=2010-05-01&rft.volume=23&rft.issue=5&rft.spage=1185&rft.epage=1197&rft.pages=1185-1197&rft.issn=0951-7715&rft.eissn=1361-6544&rft_id=info:doi/10.1088/0951-7715/23/5/009&rft_dat=%3Cproquest_pasca%3E1671236650%3C/proquest_pasca%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1671236650&rft_id=info:pmid/&rfr_iscdi=true |