2 3 Fe b 19 99 Symmetry , Hamiltonian Problems and Wavelets in Accelerator Physics

In this paper we consider applications of methods from wavelet analysis to nonlinear dynamical problems related to accelerator physics. In our approach we take into account underlying algebraical, geometrical and topological structures of corresponding problems. This paper is the sequel to our first paper in this volume [1], in which we considered the applications of a number of analytical methods from nonlinear (local) Fourier analysis, or wavelet analysis, to nonlinear accelerator physics problems. This paper is the continuation of results from [2]–[7], which is based on our approach to investigation of nonlinear problems, both general and with additional structures (Hamiltonian, symplectic or quasicomplex), chaotic, quasiclassical, and quantum. Wavelet analysis is a relatively novel set of mathematical methods, which gives us the possibility of working with well-localized bases in functional spaces and with the general type of operators (differential, integral, pseudodifferential) in such bases. In contrast with paper [1], in this paper we try to take into account before using power analytical approaches underlying algebraical, geometrical, and topo-logical structures related to the kinematical, dynamical and hidden symmetry of physical problems. In this paper we give a review of a number of the corresponding problems and describe the key points of some possible methods by which we can find the full solutions of the initial physical problem. We describe a few concrete problems in [1, part II]. The most interesting case is the dynamics of spin-orbital motion [1, II D]. Related problems may be found in [8].