DocumentCode :
1868733
Title :
Hamiltonian problems via wavelets
Author :
Fedorova, Antonina N. ; Zeitlin, Michael G.
Author_Institution :
Inst. of Problems of Mech. Eng., Acad. of Sci., St. Petersburg, Russia
Volume :
1
fYear :
1997
fDate :
27-29 Aug 1997
Firstpage :
96
Abstract :
We present applications of wavelet analysis to polynomial approximations for a number of nonlinear problems. According to the orbit method and by using construction from the geometric quantization theory we construct the symplectic and Poisson structures associated with generalized wavelets by using metaplectic structure and corresponding polarization. We consider the generalization of our variational wavelet approach to the case of Hamiltonian systems for which we need to preserve underlying symplectic or Poissonian or quasicomplex structures in any type of calculations. We use our approach for the problem of explicit calculations of Arnold-Weinstein curves via Floer variational approach from symplectic topology. The loop solutions are parametrized by the solutions of reduced algebraical problem-matrix quadratic mirror filters equations. We give wavelet characterization of symplectic Hilbert scales of spaces. We consider wavelet approach to the calculations of Melnikov functions in the theory of homoclinic chaos in perturbed Hamiltonian systems and to computations in constrained dynamical problems
Keywords :
Hilbert spaces; approximation theory; filtering theory; matrix algebra; polynomials; stochastic processes; system theory; variational techniques; wavelet transforms; Arnold-Weinstein curves; Floer variational approach; Hamiltonian problems; Melnikov functions; Poisson structure; generalized wavelets; geometric quantization theory; homoclinic chaos; matrix quadratic mirror filters equations; metaplectic structure; nonlinear problems; perturbed Hamiltonian systems; polarization; polynomial approximations; quasicomplex structures; reduced algebraical problem; symplectic Hilbert scales; symplectic structure; variational wavelet approach; wavelet analysis; wavelet characterization; Chaos; Filters; Hilbert space; Mirrors; Poisson equations; Polarization; Polynomials; Quantization; Topology; Wavelet analysis;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Control of Oscillations and Chaos, 1997. Proceedings., 1997 1st International Conference
Conference_Location :
St. Petersburg
Print_ISBN :
0-7803-4247-X
Type :
conf
DOI :
10.1109/COC.1997.633495
Filename :
633495
Link To Document :
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