Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Adiabatic invariants for strongly nonlinear dynamical systems described with complex functions


Author: L. Cveticanin
Journal: Quart. Appl. Math. 54 (1996), 407-421
MSC: Primary 34C29; Secondary 34C99, 70H05, 70K99
DOI: https://doi.org/10.1090/qam/1402402
MathSciNet review: MR1402402
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Abstract: In this paper the adiabatic invariants for strongly nonlinear dynamical systems with two degrees of freedom described by complex functions are obtained. The method [1] developed for dynamical systems with one degree of freedom is extended to systems with two degrees of freedom. The method is based on Noether's theory and the use of Krylov-Bogolubov-Mitropolski (KBM) and elliptic-Krylov-Bogolubov (EKB) asymptotic techniques. The adiabatic invariants for two types of strong nonlinearities are constructed: the pure cubic nonlinearity and quasi-cubic nonlinearity. The adiabatic invariants are used to obtain the approximate solution to the equations of motion.


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Additional Information

DOI: https://doi.org/10.1090/qam/1402402
Article copyright: © Copyright 1996 American Mathematical Society


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