dorsal/arxiv
View SchemaNormal Form, Symmetry and Infinite Dimensional Lie Algebra for System of Ode's
| Authors | Yuji Kodama |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9404006 |
| URL | https://arxiv.org/abs/patt-sol/9404006 |
| DOI | 10.1016/0375-9601(94)90130-9 |
Abstract
The normal form for a system of ode's is constructed from its polynomial symmetries of the linear part of the system, which is assumed to be semi-simple. The symmetries are shown to have a simple structure such as invariant function times symmetries of degree one called basic symmetries. We also show that the set of symmetries naturally forms an infinite dimensional Lie algebra graded by the degree of invariant polynomials. This implies that if this algebra is non-commutative then the method of multiple scales with more than two scaling variables fails to apply.
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"abstract": "The normal form for a system of ode\u0027s is constructed from its polynomial\nsymmetries of the linear part of the system, which is assumed to be\nsemi-simple. The symmetries are shown to have a simple structure such as\ninvariant function times symmetries of degree one called basic symmetries. We\nalso show that the set of symmetries naturally forms an infinite dimensional\nLie algebra graded by the degree of invariant polynomials. This implies that if\nthis algebra is non-commutative then the method of multiple scales with more\nthan two scaling variables fails to apply.",
"arxiv_id": "patt-sol/9404006",
"authors": [
"Yuji Kodama"
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],
"doi": "10.1016/0375-9601(94)90130-9",
"title": "Normal Form, Symmetry and Infinite Dimensional Lie Algebra for System of Ode\u0027s",
"url": "https://arxiv.org/abs/patt-sol/9404006"
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