We present applications of the methods from wavelet analysis to a number of Hamiltonian problems and their perturbations, KAM problems, quantization problems. We consider dynamical problems in invariant variational approach via coadjoint orbit picture, semiproducts and metaplectic structure. We construct symplectic, Poisson and quasicomplex structures using generalized wavelets and non-standard representations for operators in wavelet bases (coherent, well localized) in functional spaces or scale of spaces. We consider applications of our approach to the theory of homoclinic chaos, renormalization group calculations and quasiclassics.
Russian Academy of Sciences, Institute of Problems of Mechanical
Engineering, V.O., Bolshoj pr., 61,
199178, St. Petersburg, Russia
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