BROWSE

Related Scientist

oh,yonggeun's photo.

oh,yonggeun
기하학수리물리연구단
more info

ITEM VIEW & DOWNLOAD

Continuous Hamiltonian dynamics and area-preserving homeomorphism group of D2

Cited 1 time in webofscience Cited 2 time in scopus
1,539 Viewed 217 Downloaded
Title
Continuous Hamiltonian dynamics and area-preserving homeomorphism group of D2
Author(s)
Yong-Geun Oh
Subject
area-preserving homeomorphism group, Calabi invariant, Lagrangian submanifolds, generating function, basic phase function, topological Hamiltonian loop, Hamilton-Jacobi equation
Publication Date
2016-07
Journal
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, v.53, no.4, pp.195 - 834
Publisher
KOREAN MATHEMATICAL SOC
Abstract
The main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group HomeoΩ(D2 , ∂D2 ) of area pre- serving homeomorphisms of the 2-disc D2. We first establish the exis- tence of Alexander isotopy in the category of Hamiltonian homeomor- phisms. This reduces the question of extendability of the well-known Calabi homomorphism Cal : DiffΩ(D1 , ∂D2) → R to a homomorphism Cal : Hameo(D2 , ∂D2 ) → R to that of the vanishing of the basic phase function fF, a Floer theoretic graph selector constructed in [9], that is associated to the graph of the topological Hamiltonian loop and its nor- malized Hamiltonian F on S2 that is obtained via the natural embedding D2 ֒→ S2. Here Hameo(D2, ∂D2 ) is the group of Hamiltonian homeo- morphisms introduced by Mu¨ller and the author [18]. We then provide an evidence of this vanishing conjecture by proving the conjecture for the special class of weakly graphical topological Hamiltonian loops on D2 via the associated Hamiton-Jacobi equation. c 2016 Korean Mathematical Society
URI
https://pr.ibs.re.kr/handle/8788114/2716
DOI
10.4134/JKMS.j150288
ISSN
0304-9914
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
Files in This Item:
2016_YGO_Continuous Hamiltonian dynamics and area-preserving homeomorphism group of D2.pdfDownload

qrcode

  • facebook

    twitter

  • Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
해당 아이템을 이메일로 공유하기 원하시면 인증을 거치시기 바랍니다.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Browse