Solving for the Fixed Points of 3-Cycle in the Logistic Map and Toward Realizing Chaos by the Theorems of Sharkovskii and Li—Yorke

Sharkovskii proved that, for continuous maps on intervals, the existence of 3-cycle implies the existence of all others. Li and Yorke proved that 3-cycle implies chaos. To establish a domain of uncountable cycles in the logistic map and to understand chaos in it, the fixed points of 3-cycle are obta...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Communications in theoretical physics 2014-10, Vol.62 (4), p.485-496
1. Verfasser:	Howard Lee, M.
Format:	Artikel
Sprache:	eng
Schlagworte:	Chaos theory Fixed points (mathematics) Intervals Lithium Logistics Mathematical analysis Theorems Theoretical physics
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page	496
container_issue	4
container_start_page	485
container_title	Communications in theoretical physics
container_volume	62
creator	Howard Lee, M.
description	Sharkovskii proved that, for continuous maps on intervals, the existence of 3-cycle implies the existence of all others. Li and Yorke proved that 3-cycle implies chaos. To establish a domain of uncountable cycles in the logistic map and to understand chaos in it, the fixed points of 3-cycle are obtained analytically by solving a sextic equation. At one parametric value, a fixed-point spectrum, resulted from the Sharkovskii limit, helps to realize chaos in the sense of Li and Yorke.
doi_str_mv	10.1088/0253-6102/62/4/06
format	Article
fullrecord	<record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1808095755</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1808095755</sourcerecordid><originalsourceid>FETCH-LOGICAL-c278t-250fc7fa58d7e73e8d9e96cb1fd42fbb968c8a032fe1c6239bae37c125dfdaf73</originalsourceid><addsrcrecordid>eNo9kLFOwzAURS0EEqXwAWweWUJtJ7GdEVUUkIpAtAxMluM8t6ZpXOy0UCYGPoEv5EugLWJ6wz3vDAehU0rOKZGyR1ieJpwS1uOsl_UI30MdmguWFFmR7aPO_36IjmJ8JoQwwWkHfY58vXLNBFsfcDsFPHBvUOF775o2Ym9xmvTXpgbsmu089BMXW2fwrV5g3VR47F91qPAD6Nq9b0T9qfYRl-stPp6CDzDfmkZTHWZ-FWfObT-H7vvj68mHGRyjA6vrCCd_t4seB5fj_nUyvLu66V8ME8OEbBOWE2uE1bmsBIgUZFVAwU1JbZUxW5YFl0ZqkjIL1HCWFqWGVBjK8spW2oq0i8523kXwL0uIrZq7aKCudQN-GRWVRJIiF3n-i9IdaoKPMYBVi-DmOqwVJWpTXG2Kqk1RxZnKFOHpD3ztdcM</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1808095755</pqid></control><display><type>article</type><title>Solving for the Fixed Points of 3-Cycle in the Logistic Map and Toward Realizing Chaos by the Theorems of Sharkovskii and Li—Yorke</title><source>IOP Publishing Journals</source><source>Institute of Physics (IOP) Journals - HEAL-Link</source><source>Alma/SFX Local Collection</source><creator>Howard Lee, M.</creator><creatorcontrib>Howard Lee, M.</creatorcontrib><description>Sharkovskii proved that, for continuous maps on intervals, the existence of 3-cycle implies the existence of all others. Li and Yorke proved that 3-cycle implies chaos. To establish a domain of uncountable cycles in the logistic map and to understand chaos in it, the fixed points of 3-cycle are obtained analytically by solving a sextic equation. At one parametric value, a fixed-point spectrum, resulted from the Sharkovskii limit, helps to realize chaos in the sense of Li and Yorke.</description><identifier>ISSN: 0253-6102</identifier><identifier>EISSN: 1572-9494</identifier><identifier>DOI: 10.1088/0253-6102/62/4/06</identifier><language>eng</language><subject>Chaos theory ; Fixed points (mathematics) ; Intervals ; Lithium ; Logistics ; Mathematical analysis ; Theorems ; Theoretical physics</subject><ispartof>Communications in theoretical physics, 2014-10, Vol.62 (4), p.485-496</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c278t-250fc7fa58d7e73e8d9e96cb1fd42fbb968c8a032fe1c6239bae37c125dfdaf73</citedby><cites>FETCH-LOGICAL-c278t-250fc7fa58d7e73e8d9e96cb1fd42fbb968c8a032fe1c6239bae37c125dfdaf73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Howard Lee, M.</creatorcontrib><title>Solving for the Fixed Points of 3-Cycle in the Logistic Map and Toward Realizing Chaos by the Theorems of Sharkovskii and Li—Yorke</title><title>Communications in theoretical physics</title><description>Sharkovskii proved that, for continuous maps on intervals, the existence of 3-cycle implies the existence of all others. Li and Yorke proved that 3-cycle implies chaos. To establish a domain of uncountable cycles in the logistic map and to understand chaos in it, the fixed points of 3-cycle are obtained analytically by solving a sextic equation. At one parametric value, a fixed-point spectrum, resulted from the Sharkovskii limit, helps to realize chaos in the sense of Li and Yorke.</description><subject>Chaos theory</subject><subject>Fixed points (mathematics)</subject><subject>Intervals</subject><subject>Lithium</subject><subject>Logistics</subject><subject>Mathematical analysis</subject><subject>Theorems</subject><subject>Theoretical physics</subject><issn>0253-6102</issn><issn>1572-9494</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNo9kLFOwzAURS0EEqXwAWweWUJtJ7GdEVUUkIpAtAxMluM8t6ZpXOy0UCYGPoEv5EugLWJ6wz3vDAehU0rOKZGyR1ieJpwS1uOsl_UI30MdmguWFFmR7aPO_36IjmJ8JoQwwWkHfY58vXLNBFsfcDsFPHBvUOF775o2Ym9xmvTXpgbsmu089BMXW2fwrV5g3VR47F91qPAD6Nq9b0T9qfYRl-stPp6CDzDfmkZTHWZ-FWfObT-H7vvj68mHGRyjA6vrCCd_t4seB5fj_nUyvLu66V8ME8OEbBOWE2uE1bmsBIgUZFVAwU1JbZUxW5YFl0ZqkjIL1HCWFqWGVBjK8spW2oq0i8523kXwL0uIrZq7aKCudQN-GRWVRJIiF3n-i9IdaoKPMYBVi-DmOqwVJWpTXG2Kqk1RxZnKFOHpD3ztdcM</recordid><startdate>201410</startdate><enddate>201410</enddate><creator>Howard Lee, M.</creator><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>201410</creationdate><title>Solving for the Fixed Points of 3-Cycle in the Logistic Map and Toward Realizing Chaos by the Theorems of Sharkovskii and Li—Yorke</title><author>Howard Lee, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c278t-250fc7fa58d7e73e8d9e96cb1fd42fbb968c8a032fe1c6239bae37c125dfdaf73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Chaos theory</topic><topic>Fixed points (mathematics)</topic><topic>Intervals</topic><topic>Lithium</topic><topic>Logistics</topic><topic>Mathematical analysis</topic><topic>Theorems</topic><topic>Theoretical physics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Howard Lee, M.</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Communications in theoretical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Howard Lee, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Solving for the Fixed Points of 3-Cycle in the Logistic Map and Toward Realizing Chaos by the Theorems of Sharkovskii and Li—Yorke</atitle><jtitle>Communications in theoretical physics</jtitle><date>2014-10</date><risdate>2014</risdate><volume>62</volume><issue>4</issue><spage>485</spage><epage>496</epage><pages>485-496</pages><issn>0253-6102</issn><eissn>1572-9494</eissn><abstract>Sharkovskii proved that, for continuous maps on intervals, the existence of 3-cycle implies the existence of all others. Li and Yorke proved that 3-cycle implies chaos. To establish a domain of uncountable cycles in the logistic map and to understand chaos in it, the fixed points of 3-cycle are obtained analytically by solving a sextic equation. At one parametric value, a fixed-point spectrum, resulted from the Sharkovskii limit, helps to realize chaos in the sense of Li and Yorke.</abstract><doi>10.1088/0253-6102/62/4/06</doi><tpages>12</tpages></addata></record>
fulltext	fulltext
identifier	ISSN: 0253-6102
ispartof	Communications in theoretical physics, 2014-10, Vol.62 (4), p.485-496
issn	0253-6102 1572-9494
language	eng
recordid	cdi_proquest_miscellaneous_1808095755
source	IOP Publishing Journals; Institute of Physics (IOP) Journals - HEAL-Link; Alma/SFX Local Collection
subjects	Chaos theory Fixed points (mathematics) Intervals Lithium Logistics Mathematical analysis Theorems Theoretical physics
title	Solving for the Fixed Points of 3-Cycle in the Logistic Map and Toward Realizing Chaos by the Theorems of Sharkovskii and Li—Yorke
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-06T19%3A33%3A55IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Solving%20for%20the%20Fixed%20Points%20of%203-Cycle%20in%20the%20Logistic%20Map%20and%20Toward%20Realizing%20Chaos%20by%20the%20Theorems%20of%20Sharkovskii%20and%20Li%E2%80%94Yorke&rft.jtitle=Communications%20in%20theoretical%20physics&rft.au=Howard%20Lee,%20M.&rft.date=2014-10&rft.volume=62&rft.issue=4&rft.spage=485&rft.epage=496&rft.pages=485-496&rft.issn=0253-6102&rft.eissn=1572-9494&rft_id=info:doi/10.1088/0253-6102/62/4/06&rft_dat=%3Cproquest_cross%3E1808095755%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1808095755&rft_id=info:pmid/&rfr_iscdi=true