| fullrecord |
[{"key": "dc.contributor.advisor", "value": "Parkkonen Jouni", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Kek\u00e4l\u00e4inen, Annamari", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2015-10-03T17:21:49Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2015-10-03T17:21:49Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2015", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1496864", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/47245", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 tutkielmassa perehdyt\u00e4\u00e4n ympyr\u00e4dynamiikkaan, jota tutkitaan kiertojen\r\navulla. Kiertojen analysointiin k\u00e4ytet\u00e4\u00e4n pisteiden ratoja ja jaksollisia pisteit\u00e4. Tutkielmassa\r\ntutustutaan my\u00f6s nostoihin ja kiertolukuihin. Homeomorfismien k\u00e4ytt\u00e4ytymist\u00e4\r\ntutkitaan kiertoluvun avulla. Jos kiertoluku on rationaalinen, radan k\u00e4yt\u00e4ytyminen\r\non jaksollista. Jos taas kiertoluku on irrationaalinen, niin pisteen rata on\r\ntihe\u00e4 tai Cantorin joukko.\r\nTutkielmassa todistetaan Poincar`en luokittelulause, joka kuvailee ympyr\u00e4homeomorfismien\r\nratojen k\u00e4ytt\u00e4ytymist\u00e4. Poincar\u00b4en luokittelulauseen mukaan homeomor-\r\nfismi f, jonka kiertoluku \u03c1 on irrationaalinen, on topologinen konjugaatti kierron R\u03c1\r\nkanssa, jos homeomorfismi on transitiivinen. Jos homeomorfismi ei ole transitiivinen,\r\nniin kierto ja homeomorfismi ovat topologisia tekij\u00f6it\u00e4. Toisessa luvussa tutustutaan\r\nDenjoyn esimerkkiin ja lauseeseen. Denjoyn lause liittyy diffeomorfismeihin. Sen mukaan\r\ndiffeomorfismi on transitiivinen, jos sen kiertoluku on irrationaalinen ja derivaatta\r\non rajoitetusti heilahteleva. Denjoyn esimerkiss\u00e4a n\u00e4ytet\u00e4\u00e4n, kuinka modostetaan\r\nilman jaksollisia pisteit\u00e4 ympyr\u00e4diffeomorfismi, joka ei ole transitiivinen. Kolmannessa\r\nluvussa tutustutaan Cantorin joukkoon, pirunporrasfunktioon ja Arnoldin kieliin\r\nympyr\u00e4adiffeomorfismiperheiden kautta.", "language": "", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Annamari Kek\u00e4l\u00e4inen (anjokeka) on 2015-10-03 17:21:45.666377. Form: Pro gradu -lomake (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake). JyX data: [jyx_publishing-allowed (fi) =True]", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija.group@korppi.jyu.fi) on 2015-10-03T17:21:49Z\nNo. of bitstreams: 2\nURN:NBN:fi:jyu-201510033305.pdf: 4479684 bytes, checksum: 34f74777ec0ce4e2ccca2ba67325cb48 (MD5)\nlicense.html: 4808 bytes, checksum: ee65f2222cb9d4611cf379e157ff0607 (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2015-10-03T17:21:49Z (GMT). No. of bitstreams: 2\nURN:NBN:fi:jyu-201510033305.pdf: 4479684 bytes, checksum: 34f74777ec0ce4e2ccca2ba67325cb48 (MD5)\nlicense.html: 4808 bytes, checksum: ee65f2222cb9d4611cf379e157ff0607 (MD5)\n Previous issue date: 2015", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (58 sivua)", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "kiertoluku", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "ympyr\u00e4", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "homeomorfismi", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "diffeomorfismi", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "pirunporrasfunktio", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Ympyr\u00e4n homeomorfismien dynamiikkaa", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-201510033305", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.date.updated", "value": "2015-10-03T17:21:50Z", "language": null, "element": "date", "qualifier": "updated", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": null, "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": "fi", "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": null, "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
|