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Kolmogorov algorithm for isochronous Hamiltonian systems
Mathematics in Engineering 2023, 5(2): 1-35
Published: 15 April 2023
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We present a Kolmogorov-like algorithm for the computation of a normal form in the neighborhood of an invariant torus in 'isochronous' Hamiltonian systems, i.e., systems with Hamiltonians of the form H=H0+εH1 where H0 is the Hamiltonian of N linear oscillators, and H1 is expandable as a polynomial series in the oscillators' canonical variables. This method can be regarded as a normal form analogue of a corresponding Lindstedt method for coupled oscillators. We comment on the possible use of the Lindstedt method itself under two distinct schemes, i.e., one producing series analogous to those of the Birkhoff normal form scheme, and another, analogous to the Kolomogorov normal form scheme in which we fix in advance the frequency of the torus.

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