{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T18:49:24Z","timestamp":1767034164310,"version":"3.37.3"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100002241","name":"Japan Science and Technology Agency","doi-asserted-by":"publisher","award":["JPMJPR16E"],"award-info":[{"award-number":["JPMJPR16E"]}],"id":[{"id":"10.13039\/501100002241","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,4]]},"abstract":"<jats:p> We study the transition graph of generic Hamiltonian surface flows, whose vertices are the topological equivalence classes of generic Hamiltonian surface flows and whose edges are the generic transitions. Using the transition graph, we can describe time evaluations of generic Hamiltonian surface flows (e.g., fluid phenomena) as walks on the graph. We propose a method for constructing the complete transition graph of all generic Hamiltonian flows. In fact, we construct two complete transition graphs of Hamiltonian surface flows having three and four genus elements. Moreover, we demonstrate that a lower bound on the transition distance between two Hamiltonian surface flows with any number of genus elements can be calculated by solving an integer programming problem using vector representations of Hamiltonian surface flows. <\/jats:p>","DOI":"10.1142\/s1793830921500233","type":"journal-article","created":{"date-parts":[[2020,9,16]],"date-time":"2020-09-16T15:02:27Z","timestamp":1600268547000},"page":"2150023","source":"Crossref","is-referenced-by-count":3,"title":["Complete transition diagrams of generic Hamiltonian flows with a few heteroclinic orbits"],"prefix":"10.1142","volume":"13","author":[{"given":"Tetsuo","family":"Yokoyama","sequence":"first","affiliation":[{"name":"Department of Software Engineering, Nanzan University, Yamazato-cho 18, Showa-ku, Nagoya, Aichi 466-8673, Japan"}]},{"given":"Tomoo","family":"Yokoyama","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kyoto University of Education\/JST PRESTO, 1 Fujinomori, Fukakusa, Fushimi-ku, Kyoto 612-8522, Japan"}]}],"member":"219","published-online":{"date-parts":[[2020,10,28]]},"reference":[{"key":"S1793830921500233BIB001","series-title":"Translations of Mathematical Monographs","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/153","volume-title":"Introduction to the Qualitative Theory of Dynamical Systems on Surfaces","volume":"153","author":"Aranson S. 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