2019年10月4日 14時 45分 ～ 2019年10月4日 16時 15分
タイトル: Complete invariant of surface flows and their transitions
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 which are structurally stable in the set of Hamiltonian flows on form an open dense subset of . 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 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.