This article is cited in 4 papers

Nondegenerate Hamiltonian Hopf Bifurcations in $\omega: 3: 6$ Resonance $(\omega=1 \, \text{or}\, 2)$

Reza Mazrooei-Sebdani, Elham Hakimi

Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111 Isfahan, Iran

Abstract: This paper deals with the analysis of Hamiltonian Hopf bifurcations in three-degree-of-freedom systems, for which the frequencies of the linearization of the corresponding Hamiltonians are in $\omega: 3: 6$ resonance $(\omega=1\, \text{or}\, 2)$. We obtain the truncated second-order normal form that is not integrable and expressed in terms of the invariants of the reduced phase space. The truncated first-order normal form gives rise to an integrable system that is analyzed using a reduction to a one-degree-of-freedom system. In this paper, some detuning parameters are considered and nondegenerate Hamiltonian Hopf bifurcations are found. To study Hamiltonian Hopf bifurcations, we transform the reduced Hamiltonian into standard form.

Keywords: Hamiltonian $\omega: 3: 6$ resonance $(\omega=1\, \text{or}\, 2)$, integrability, reduction, normal forms, Hamiltonian Hopf bifurcation.

MSC: 70K30, 37J35, 70H06, 70H33, 70K45

Received: 11.01.2020
Accepted: 22.07.2020

Language: English

DOI: 10.1134/S1560354720060027

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