변양현
김주희
2020-04-08T17:04:37Z
2020-04-08T17:04:37Z
2007-08
https://repository.hanyang.ac.kr/handle/20.500.11754/148950
http://hanyang.dcollection.net/common/orgView/200000407189
Let Ｄ be an open disk in R² and consider the open subset Ｄ×R＾(n-1)×R＾(n-1) of R＾(2n) with the standard symplectic structure. Also let l_(0), l₁be two open arcs in Ｄ which are closed as subsets of Ｄ meeting each other transversely at exactly two points.
We construct a Hamiltonian flow with compact support, Ψ_(u) : Ｄ×Ｒ＾(n-1)×Ｒ＾(n-1)→Ｄ×Ｒ＾(n-1)×Ｒ＾(n-1), 0 ≤ u ≤ 1 such that Ψ_(0) = 1 and . Ψ₁(l_(0)×Ｒ＾(n-1)×0)∩(l₁×0×Ｒ＾(n-1)) = φ.
Construction of such Ψ_(u), 0 ≤ u ≤ 1, deserves called a Lagrangian Whitney trick. We will show that the condition is needed involving the areas of the regions Ｄ in divided by l_(0) and l₁for the construction.
한양대학교
라그라지안 휘트니트릭과 넓이조건
The Lagrangian Whitney Trick and The Area Condition
Theses
김주희
Kim, Ju-Hee
S
대학원
수학과
Master