2016 Fiscal Year Final Research Report
Research on integrable dynamical systems using geometric methods
Project/Area Number |
25400106
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Basic analysis
|
Research Institution | Tokyo University of Marine Science and Technology |
Principal Investigator |
|
Project Period (FY) |
2013-04-01 – 2017-03-31
|
Keywords | パンルヴェ方程式 / 力学系 / 有理曲面 / モノドロミー |
Outline of Final Research Achievements |
We have found a general explicit formula for obtaining the differential Painleve equation from monodromy preservation deformation of the Fuchs type linear ordinary differential equations. We also formulated it as a discrete Hamiltonian system. Regarding deautonomization of isomorphic mappings of a rational elliptic surfaces, we have formulated a method to derive the corresponding discrete Painleve equation to a choice of an elliptical fiber. The key to this is a method of constructing a map from the action on the Picard group, and we found a general formula for that. In addition, we have discovered symmetries which were not known so far for the simplified version of the resulting elliptic difference Painleve equations.
|
Free Research Field |
可積分系
|