{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/32055"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/32055","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Brjuno Numbers and Complex Dynamics","abstract":"The Brjuno numbers play a fundamental role in the study of the 1-dimensional Complex Dynamics Theory. In this work we examine the proof of the Brjuno theorem by using elements of Number Theory. We also examine the topological version of the proof given by J. Yoccoz and his renormalization principle. If α ∈ ℝ\\ℚ, we also describe how the existence of a Siegel disk at the origin for the polynomial P(𝑧) = exp(2πiα)·(𝑧 − 𝑧²) implies the linearization of any germ of the form 𝑓(𝑧) = exp(2πiα)·𝑧 + 𝑂(𝑧²).","abstract_html":"The Brjuno numbers play a fundamental role in the study of the 1-dimensional Complex Dynamics Theory. In this work we examine the proof of the Brjuno theorem by using elements of Number Theory. We also examine the topological version of the proof given by J. Yoccoz and his renormalization principle. If α ∈ ℝ\\ℚ, we also describe how the existence of a Siegel disk at the origin for the polynomial P(𝑧) = exp(2πiα)·(𝑧 − 𝑧²) implies the linearization of any germ of the form 𝑓(𝑧) = exp(2πiα)·𝑧 + 𝑂(𝑧²).","abstract_has_math":false,"creators":["Saenz Maldonado, Edgar Arturo"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Floyd, William J."],"committee_members":["Kay, Leslie D.","Haskell, Peter E."],"year":2008,"date_issued":"2008-04-17","date_published":"2008-04-17","updated_at":"2026-07-22T22:19:47Z","subjects":["Brjuno Numbers","Siegel Disks","Complex Dynamics"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-04302008-005312"],"render_values":[{"text":"etd-04302008-005312","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/32055","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Floyd, William J."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Kay, Leslie D.","Haskell, Peter E."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Saenz Maldonado, Edgar Arturo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:34:38Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:34:38Z","2008-05-14"]},{"key":"dc:date.issued","label":"Date","values":["2008-04-17"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Brjuno Numbers","Siegel Disks","Complex Dynamics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-04302008-005312"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/32055"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Brjuno numbers play a fundamental role in the study of the 1-dimensional Complex Dynamics Theory. In this work we examine the proof of the Brjuno theorem by using elements of Number Theory. We also examine the topological version of the proof given by J. Yoccoz and his renormalization principle. If α ∈ ℝ\\ℚ, we also describe how the existence of a Siegel disk at the origin for the polynomial P(𝑧) = exp(2πiα)·(𝑧 − 𝑧²) implies the linearization of any germ of the form 𝑓(𝑧) = exp(2πiα)·𝑧 + 𝑂(𝑧²)."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["Brjuno Numbers and Complex Dynamics"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Floyd, William J."],"dc:contributor.committeemember":["Kay, Leslie D.","Haskell, Peter E."],"dc:contributor.department":["Mathematics"],"dc:creator":["Saenz Maldonado, Edgar Arturo"],"dc:date.accessioned":["2014-03-14T20:34:38Z"],"dc:date.available":["2014-03-14T20:34:38Z","2008-05-14"],"dc:date.issued":["2008-04-17"],"dc:description.abstract":["The Brjuno numbers play a fundamental role in the study of the 1-dimensional Complex Dynamics Theory. In this work we examine the proof of the Brjuno theorem by using elements of Number Theory. We also examine the topological version of the proof given by J. Yoccoz and his renormalization principle. If α ∈ ℝ\\ℚ, we also describe how the existence of a Siegel disk at the origin for the polynomial P(𝑧) = exp(2πiα)·(𝑧 − 𝑧²) implies the linearization of any germ of the form 𝑓(𝑧) = exp(2πiα)·𝑧 + 𝑂(𝑧²)."],"dc:description.degree":["Master of Science"],"dc:identifier.other":["etd-04302008-005312"],"dc:identifier.uri":["http://hdl.handle.net/10919/32055"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Brjuno Numbers","Siegel Disks","Complex Dynamics"],"dc:title":["Brjuno Numbers and Complex Dynamics"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:47Z"}