# On the topology of nearly-integrable Hamiltonians at simple resonances

@article{Biasco2020OnTT,
title={On the topology of nearly-integrable Hamiltonians at simple resonances},
author={Luca Biasco and Luigi Chierchia},
journal={Nonlinearity},
year={2020}
}
• Published 22 July 2019
• Mathematics
• Nonlinearity
We show that, in general, averaging at simple resonances a real--analytic, nearly--integrable Hamiltonian, one obtains a one--dimensional system with a cosine--like potential; in general'' means for a generic class of holomorphic perturbations and apart from a finite number of simple resonances with small Fourier modes; cosine--like'' means that the potential depends only on the resonant angle, with respect to which it is a Morse function with one maximum and one minimum. \\ Furthermore… Expand
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