{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/30907"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/30907","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The order of growth of the fourth painleve transcendents","abstract":"Let w be a transcendental solution of the fourth Painlevé equation w00 = (w0)2 2w + 3 2 w3 + 4zw2 + 2(z2 􀀀 )w + w : It has a rst integral w02 = w4 + 4zw3 + 4(z2 􀀀 )w2 􀀀 2 􀀀 4wU; where the auxilliary function U satis es U0 = w2 + 2zw: We will consider three speci c cases of limit behaviors of the auxiliary function U outside certain exceptional sets. In each case, we conclude that w is either of order (w) = 2 or of order (w) = 4: ii","abstract_html":"Let w be a transcendental solution of the fourth Painlevé equation w00 = (w0)2 2w + 3 2 w3 + 4zw2 + 2(z2 􀀀 )w + w : It has a rst integral w02 = w4 + 4zw3 + 4(z2 􀀀 )w2 􀀀 2 􀀀 4wU; where the auxilliary function U satis es U0 = w2 + 2zw: We will consider three speci c cases of limit behaviors of the auxiliary function U outside certain exceptional sets. In each case, we conclude that w is either of order (w) = 2 or of order (w) = 4: ii","abstract_has_math":false,"creators":["Sriponpaew, Boonyong"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Hinkkanen, Aimo","Loeb, Peter","Nikolaev, Igor","Miles, Joseph B."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-22T00:14:28Z","date_published":"2012-05-22T00:14:28Z","updated_at":"2026-07-22T22:25:29Z","subjects":["order of growth","fourth Painlevé equation"],"languages":["en"],"rights":["Copyright 2012 Boonyong Sriponpaew"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/30907","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hinkkanen, Aimo","Loeb, Peter","Nikolaev, Igor","Miles, Joseph B."]},{"key":"dc:creator","label":"Author","values":["Sriponpaew, Boonyong"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-05-22T00:14:28Z","2012-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["order of growth","fourth Painlevé equation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2012 Boonyong Sriponpaew"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/30907"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Let w be a transcendental solution of the fourth Painlevé equation w00 = (w0)2 2w + 3 2 w3 + 4zw2 + 2(z2 􀀀 )w + w : It has a rst integral w02 = w4 + 4zw3 + 4(z2 􀀀 )w2 􀀀 2 􀀀 4wU; where the auxilliary function U satis es U0 = w2 + 2zw: We will consider three speci c cases of limit behaviors of the auxiliary function U outside certain exceptional sets. In each case, we conclude that w is either of order (w) = 2 or of order (w) = 4: ii","Item withdrawn by Rebecca Bryant (rabryant@illinois.edu) on 2012-04-18T20:16:59Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Sriponpaew_Boonyong.pdf: 616365 bytes, checksum: 2d88e252aa5f5a1f971f4171dd784d05 (MD5)","Made available in DSpace on 2012-05-22T00:14:28Z (GMT). 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In each case, we conclude that w is either of order (w) = 2 or of order (w) = 4: ii","Item withdrawn by Rebecca Bryant (rabryant@illinois.edu) on 2012-04-18T20:16:59Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Sriponpaew_Boonyong.pdf: 616365 bytes, checksum: 2d88e252aa5f5a1f971f4171dd784d05 (MD5)","Made available in DSpace on 2012-05-22T00:14:28Z (GMT). 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