| 研究開始時の研究の概要 |
When using mathematical models in science, problems often boil down to solving equations. Unfortunately, in many cases the equations cannot be solved exactly and the systems they describe are chaotic due to nonlinearity. However, there are special nonlinear examples known as integrable systems which exhibit regular behaviour. Often this can be explained in terms of some underlying geometric structure, for example in the case of discrete Painleve equations. This project will study examples of discrete Painleve equations in higher dimensions with a view to developing a geometric theory of them.
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