応用特異点論ラボセミナー：Complete invariant of surface flows and their transitions（横山知郎氏，京都教育大学）

開催日時

2019年10月4日 14時 45分 ～ 2019年10月4日 16時 15分

場所

北海道大学理学部3号館210室

講演者

横山 知郎（京都教育大学）

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.