dorsal/arxiv
View SchemaThe Stackel systems and algebraic curves
| Authors | A. V. Tsiganov |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9712003 |
| URL | https://arxiv.org/abs/solv-int/9712003 |
Abstract
We show how the Abel-Jacobi map provides all the principal properties of an ample family of integrable mechanical systems associated to hyperelliptic curves. We prove that derivative of the Abel-Jacobi map is just the St\"{a}ckel matrix, which determines $n$-orthogonal curvilinear coordinate systems in a flat space. The Lax pairs, $r$-matrix algebras and explicit form of the flat coordinates are constructed. An application of the Weierstrass reduction theory allows to construct several flat coordinate systems on a common hyperelliptic curve and to connect among themselves different integrable systems on a single phase space.
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"abstract": "We show how the Abel-Jacobi map provides all the principal properties of an\nample family of integrable mechanical systems associated to hyperelliptic\ncurves. We prove that derivative of the Abel-Jacobi map is just the St\\\"{a}ckel\nmatrix, which determines $n$-orthogonal curvilinear coordinate systems in a\nflat space. The Lax pairs, $r$-matrix algebras and explicit form of the flat\ncoordinates are constructed. An application of the Weierstrass reduction theory\nallows to construct several flat coordinate systems on a common hyperelliptic\ncurve and to connect among themselves different integrable systems on a single\nphase space.",
"arxiv_id": "solv-int/9712003",
"authors": [
"A. V. Tsiganov"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "The Stackel systems and algebraic curves",
"url": "https://arxiv.org/abs/solv-int/9712003"
},
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