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2013
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# Reza Mazrooei-Sebdani

Isfahan University of Technology

## Publications:

 Mazrooei-Sebdani R., Hakimi E. Nondegenerate Hamiltonian Hopf Bifurcations in $\omega : 3 : 6$ Resonance $(\omega = 1$ or $2)$ 2020, vol. 25, no. 6, pp.  522-536 Abstract This paper deals with the analysis of Hamiltonian Hopf bifurcations in threedegree- of-freedom systems, for which the frequencies of the linearization of the corresponding Hamiltonians are in $\omega : 3 : 6$ resonance $(\omega = 1$ 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 $(\omega = 1$ or $2)$, integrability, reduction, normal forms, Hamiltonian Hopf bifurcation Citation: Mazrooei-Sebdani R., Hakimi E.,  Nondegenerate Hamiltonian Hopf Bifurcations in $\omega : 3 : 6$ Resonance $(\omega = 1$ or $2)$, Regular and Chaotic Dynamics, 2020, vol. 25, no. 6, pp. 522-536 DOI:10.1134/S1560354720060027