dorsal/arxiv
View SchemaNonlinear Dynamics of Accelerator via Wavelet Approach
| Authors | Antonina N. Fedorova, Michael G. Zeitlin |
|---|---|
| Categories | |
| ArXiv ID | physics/9710035 |
| URL | https://arxiv.org/abs/physics/9710035 |
| DOI | 10.1063/1.53488 |
| Journal | American Institute of Physics,Conference Proc.,Beam Stability and Nonlinear Dynamics,vol.405,pp.87-102,1997 |
Abstract
In this paper we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In the general case we have the solution as a multiresolution expansion in the base of compactly supported wavelet basis. The solution is parametrized by the solutions of two reduced algebraical problems, one is nonlinear and the second is some linear problem, which is obtained from one of the next wavelet constructions: Fast Wavelet Transform, Stationary Subdivision Schemes, the method of Connection Coefficients. According to the orbit method and by using construction from the geometric quantization theory we construct the symplectic and Poisson structures associated with generalized wavelets by using metaplectic structure. We consider wavelet approach to the calculations of Melnikov functions in the theory of homoclinic chaos in perturbed Hamiltonian systems and for parametrization of Arnold-Weinstein curves in Floer variational approach.
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"abstract": "In this paper we present the applications of methods from wavelet analysis to\npolynomial approximations for a number of accelerator physics problems. In the\ngeneral case we have the solution as a multiresolution expansion in the base of\ncompactly supported wavelet basis. The solution is parametrized by the\nsolutions of two reduced algebraical problems, one is nonlinear and the second\nis some linear problem, which is obtained from one of the next wavelet\nconstructions: Fast Wavelet Transform, Stationary Subdivision Schemes, the\nmethod of Connection Coefficients. According to the orbit method and by using\nconstruction from the geometric quantization theory we construct the symplectic\nand Poisson structures associated with generalized wavelets by using\nmetaplectic structure. We consider wavelet approach to the calculations of\nMelnikov functions in the theory of homoclinic chaos in perturbed Hamiltonian\nsystems and for parametrization of Arnold-Weinstein curves in Floer variational\napproach.",
"arxiv_id": "physics/9710035",
"authors": [
"Antonina N. Fedorova",
"Michael G. Zeitlin"
],
"categories": [
"physics.acc-ph",
"chao-dyn",
"math-ph",
"math.MP",
"nlin.CD",
"nlin.PS",
"patt-sol",
"physics.comp-ph"
],
"doi": "10.1063/1.53488",
"journal_ref": "American Institute of Physics,Conference Proc.,Beam Stability and\n Nonlinear Dynamics,vol.405,pp.87-102,1997",
"title": "Nonlinear Dynamics of Accelerator via Wavelet Approach",
"url": "https://arxiv.org/abs/physics/9710035"
},
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