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On the integrability of Hamiltonian 1:2:2 resonance

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Abstract

We study the integrability of the Hamiltonian normal form of 1:2:2 resonance. It is known that this normal form truncated to order three is integrable. The truncated to order four normal form contains many parameters. For a generic choice of parameters in the normal form up to order four, we carry on non-integrability analysis, based on the Morales–Ramis theory using only first variational equations along certain particular solutions. The non-integrability obtained by algebraic proofs produces dynamics illustrated by some numerical experiments.We also isolate a non-trivial case of integrability.

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Acknowledgements

I would like to thank the reviewers for their suggestions which significantly improved the text. This work is partially supported by Grant DN 02-5 of Bulgarian Fund “Scientific Research.”

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  1. Faculty of Mathematics and Informatics, Sofia University, 5 J. Bouchier blvd., 1164, Sofia, Bulgaria

    Ognyan Christov

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  1. Ognyan Christov
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Correspondence to Ognyan Christov.

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Christov, O. On the integrability of Hamiltonian 1:2:2 resonance. Nonlinear Dyn 102, 2295–2309 (2020). https://doi.org/10.1007/s11071-020-06036-0

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