Pseudo-holomorphic curves and periodic orbits in Hamiltonian dynamics
| Project/Area Number |
25800041
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
Irie Kei 京都大学, 数理解析研究所, 助教 (90645467)
|
|---|
| Project Period (FY) |
2013-04-01 – 2017-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
|
| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
|---|
| Keywords | 擬正則曲線 / ハミルトン力学系 / 周期軌道 / ストリング・トポロジー / レーブ力学系 / 閉補題 / 埋込接触ホモロジー / ストリングトポロジー / フレアホモロジー |
|---|
| Outline of Final Research Achievements |
I studied applications of pseudo-holomorphic curve theory in symplectic geometry to the study of periodic orbits of Hamiltonian systems.
Main achievements are: (1). Computation of symplectic capacity of unit disk cotangent bundle of a Riemannian manifold with boundary via geometry of free loop space. As an application, a good estimate of the shortest length of periodic billiard trajectory was obtained. (2). Construction of chain-level algebraic structures in string topology, which conjecturally correspond to higher products in Floer homology of cotangent bundles. (3). Proof of C-infinity closing lemma for three-dimensional Reeb flows and two-dimensional Hamiltonian diffeomorphisms using embedded contact homology.
|
Report
(5 results)
Research Products
(21 results)
