Wavelet approach to accelerator problems. 1: Polynomial dynamics

摘要

This is the first part of a series of talks in which the authors present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In the general case they have the solution as a multiresolution expansion in the base of compactly supported wavelet basis. The solution is parameterized by 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. In this paper the authors consider the problem of calculation of orbital motion in storage rings. The key point in the solution of this problem is the use of the methods of wavelet analysis, relatively novel set of mathematical methods, which gives one a possibility to work with well-localized bases in functional spaces and with the general type of operators (including pseudodifferential) in such bases.