{'fraction_non_alphanumeric': 0.0254816656308266, 'fraction_numerical': 0.004972032318210068, 'mean_word_length': 5.544715447154472, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
WAVELET APPROACH TO HAMILTONIAN, CHAOTIC AND QUANTUM CALCULATIONS IN ACCELERATOR PHYSICS

This is the second part of two our presentations in which we consider applications of methods from wavelet analysis to nonlinear accelerator physics problems. This is a continuation of our results from [1], [2], which is based on approach of two of us from [3], [4] to investigation of nonlinear problems – general, with additional structures (Hamiltonian, symplectic or quasicomplex), chaotic, quasiclassical, quantum, which are considered in the framework of local(nonlinear) Fourier analysis, or wavelet analysis. Wavelet analysis is a relatively novel set of mathematical methods, which gives us a possibility to work with welllocalized bases in functional spaces and with the general type of operators (differential, integral, pseudodifferential) in such bases. Now we consider applications of very useful and powerful method of fast wavelet transform to the problems which appear in nonlinear orbital dynamics in storage rings [5]. The first problem is the explicit calculation of quasiclassical evolution which we consider in section 2 and the second problem, which we consider in section 3, is calculations in (perturbed) Hamiltonian systems in cases when we need to consider multiresolution expansion not in one functional space but in infinite scale of spaces with underlying symplectic structure. In section 4 we consider the key point of this approach which gives useful maximally sparse representation of differential operator that allows us to take into account contribution from each level of resolution.