We present the applications of methods from wavelet analysis to polynomial approximations for a number of nonlinear problems. According to the orbit method and by using approach from the geometric quantization theory we construct the symplecticand 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, for parametrization ofArnold-Weinstein curves in Floer variational approach and characterization of symplectic Hilbert scales of spaces.
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