{"id":{"repo_id":"siu-theses","oai_identifier":"oai:opensiuc.lib.siu.edu:dissertations-2295"},"canonical_url":"https://search.dev.ndltd.org/etd/siu-theses/oai:opensiuc.lib.siu.edu:dissertations-2295","repository":{"repo_id":"siu-theses","name":"Southern Illinois University","base_url":"https://opensiuc.lib.siu.edu/do/oai/"},"display":{"title":"A ZETA FUNCTION FOR FLOWS WITH L(−1,−1) TEMPLATE","abstract":"In this dissertation, we study the flows on R3 associated with a nonlinear system differential equation introduced by Clark Robinson in [46]. The periodic orbits are modeled by a semi-flow on the L(−1,−1) template. It is known that these are positive knots, but need not have positive braid presentations. Here we prove that they are fibered. We investigate their linking and we construct a zeta-function that counts periodic orbits according to their twisting. This extends work by M. Sullivan in [55], and [57].","abstract_html":"In this dissertation, we study the flows on R3 associated with a nonlinear system differential equation introduced by Clark Robinson in [46]. The periodic orbits are modeled by a semi-flow on the L(−1,−1) template. It is known that these are positive knots, but need not have positive braid presentations. Here we prove that they are fibered. We investigate their linking and we construct a zeta-function that counts periodic orbits according to their twisting. This extends work by M. Sullivan in [55], and [57].","abstract_has_math":false,"creators":["AL-Hashimi, Ghazwan Mohammed"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Campus Only Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["SULLIVAN, MICHAEL"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-12-01T08:00:00Z","date_published":"2016-12-01T08:00:00Z","updated_at":"2026-07-24T04:35:08Z","subjects":["Alexander polynomial of knots","Fibered Knots","Lorenz Template and Lorenz-like templates","Positive knots and positive braids","Smale Flows","Zeta function"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opensiuc.lib.siu.edu/dissertations/1291","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["SULLIVAN, MICHAEL"]},{"key":"dc:creator","label":"Author","values":["AL-Hashimi, Ghazwan Mohammed"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Campus Only Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Alexander polynomial of knots","Fibered Knots","Lorenz Template and Lorenz-like templates","Positive knots and positive braids","Smale Flows","Zeta function"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://opensiuc.lib.siu.edu/dissertations/1291"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this dissertation, we study the flows on R3 associated with a nonlinear system differential equation introduced by Clark Robinson in [46]. The periodic orbits are modeled by a semi-flow on the L(−1,−1) template. It is known that these are positive knots, but need not have positive braid presentations. Here we prove that they are fibered. We investigate their linking and we construct a zeta-function that counts periodic orbits according to their twisting. This extends work by M. Sullivan in [55], and [57]."]},{"key":"dc:title","label":"Title","values":["A ZETA FUNCTION FOR FLOWS WITH L(−1,−1) TEMPLATE"]}]}],"canonical_facts":{"dc:contributor":["SULLIVAN, MICHAEL"],"dc:creator":["AL-Hashimi, Ghazwan Mohammed"],"dc:description.abstract":["In this dissertation, we study the flows on R3 associated with a nonlinear system differential equation introduced by Clark Robinson in [46]. The periodic orbits are modeled by a semi-flow on the L(−1,−1) template. It is known that these are positive knots, but need not have positive braid presentations. Here we prove that they are fibered. We investigate their linking and we construct a zeta-function that counts periodic orbits according to their twisting. This extends work by M. Sullivan in [55], and [57]."],"dc:identifier":["https://opensiuc.lib.siu.edu/dissertations/1291"],"dc:subject":["Alexander polynomial of knots","Fibered Knots","Lorenz Template and Lorenz-like templates","Positive knots and positive braids","Smale Flows","Zeta function"],"dc:title":["A ZETA FUNCTION FOR FLOWS WITH L(−1,−1) TEMPLATE"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Campus Only Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T04:35:08Z"}