Symmetry Reduction by Lifting for Maps
| Autor: | Dullin, H. R., Lomeli, H. E., Meiss, J. D. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Nonlinearity 25, 1709-1733 (2012) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/0951-7715/25/6/1709 |
| Popis: | We study diffeomorphisms that have one-parameter families of continuous symmetries. For general maps, in contrast to the symplectic case, existence of a symmetry no longer implies existence of an invariant. Conversely, a map with an invariant need not have a symmetry. We show that when a symmetry flow has a global Poincar\'{e} section there are coordinates in which the map takes a reduced, skew-product form, and hence allows for reduction of dimensionality. We show that the reduction of a volume-preserving map again is volume preserving. Finally we sharpen the Noether theorem for symplectic maps. A number of illustrative examples are discussed and the method is compared with traditional reduction techniques. Comment: laTeX, 31 pages, 5 figures |
| Databáze: | arXiv |
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