[geometry-ml:03832] 第２０回応用特異点論ラボ・セミナーのお知らせ

[izumiya ＠ math.sci.hokudai.ac.jp]

幾何学分科会 メールリストの皆様

北海道大学の泉屋です。応用特異点ラボ・セミナーのお知らせです
応用特異点ラボのホームページ：

https://sites.google.com/site/appliedsingularitytheorylab (https://sites.google.com/site/appliedsingularitytheorylab)
	開催日時：2019年10月04日14時45分～16時15分、 場所： 北海道大学理学部3号館210室

後援者：横山知郎氏（京都教育大学）

講演タイトル： Complete invariant of surface flows and their transitions、

アブストラクト：

	This talk is based on a following question: What is a generic transition of flows on compact surfaces? In particular, which kind of singular points are generic? One of goal of this talk is describing an answer for Hamiltonian case. Indeed, it's known that Hamiltonian flows on a compact surface MM which are structurally stable in the set HH of Hamiltonian flows on MM form an open dense subset of HH. Hence we need "suitable" unstable Hamiltonian flows between structurally stable Hamiltonian flows to describe a time evolution of time dependent Hamiltonian flows (e.g. a solution of Navier-Stokes equation). In other words, we need a subset of HH in which reasonable transitions are generic to describe "suitable" generic transitions. Thus we introduce a classification of evaluations and "natural" transitions to describe time evaluations of Hamiltonian flows. In particular, we give some examples to understand what are transitions. Moreover, we introduce a complete invariant which is a pair of a word and a combinatorial structure, called a COT representation and a linking structure, for more general flows (e.g. slices of flows on three dimensional manifolds) to construct a foundation of transitions of general flows on surfaces. In particular, we illustrate the invariant using Hamiltonian flows and Morse-Smale flows.

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