Titlebook: Averaging Methods in Nonlinear Dynamical Systems; Jan A. Sanders,Ferdinand Verhulst,James Murdock Book 2007Latest edition Springer-Verlag

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Hamiltonian Normal Form Theory,After introducing some concepts of Hamiltonian systems, we will discuss normalization in a Hamiltonian context. The applications will be directed at the basic resonances of two and three degree of freedom systems.

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A 4-Dimensional Example of Hopf Bifurcation,We present here the essentials of the Hopf bifurcation theory, as far as they might be of use to the actual user, and, on the other hand, we boil down the amount of computations needed, to the point where they will not present the reason for not computing anything at all.

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On Averaging Methods for Partial Differential Equations,This appendix is an adaptation and extension of the paper [280].

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Methodology of Averaging,eeping” of averaging calculations, averaging systems containing “slow time”, ways to remove the nonuniqueness of the averaging transformation, and the relationship between averaging and the method of multiple scales.

Institution

Attraction,tances. Usually the error estimates are valid for a time of order 1/., although occasionally this can be extended to 1/. for some integer . > 1 (see Theorem 2.9.4). In this chapter and the next, we investigate circumstances under which the validity of averaging can be extended still farther. Results

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Passage Through Resonance, could not happen, that is, Ω.(x) does not vanish, calling this the regular case. We now return to the problem where Ω. can have zeros or can be small. We cannot present a complete theory as such a theory is not available, so we rather aim at introducing the reader to the relevant concepts. This may

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