2013 Fiscal Year Final Research Report
Studies on the geometry of discrete integrable systems and solvable chaotic systems
| Project/Area Number |
22740100
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Chiba University |
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Principal Investigator |
NOBE Atsushi 千葉大学, 教育学部, 准教授 (80397728)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 可積分系 / トロピカル幾何学 |
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| Research Abstract |
We establish a geometric realization of the periodic discrete Toda lattice of an arbitrary system size by using the intersection of its spectral curve and other two curves. This realization is reduced from the addition of points on the symmetric product of the spectral curve, and the curves in the realization are concretely given by using the conserved quantities of the periodic discrete Toda lattice.
We also establish a geometric realization of the ultradiscrete periodic Toda lattice of an arbitrary system size, which is an ultradiscrete analogue of the periodic discrete Toda lattice, via tropical plane curves. The tropical curves in the realization, one of which is the spectral curve of the ultradiscrete periodic Toda lattice (a tropical hyperelliptic curve), are also given by using the conserved quantities of the ultradiscrete periodic Toda lattice.
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