On detuned 1:1:3 Hamiltonian resonance with cases of symmetric cubic and quartic potentials. (English) Zbl 1451.37084
Summary: This paper deals with a normal form of Hamiltonian \(1\):\(1\):\(3\) resonance. It is not integrable, and we write it using the basic invariants. Also, we identify the coefficients of the terms that remain in the normalization procedure. Then, by choosing different potential functions, we consider three integrable subfamilies of the Hamiltonian with a discrete symmetry. They are containing a Hamiltonian in a 3D Greene case, a generalized Hénon-Heiles Hamiltonian, and a quartic Hamiltonian. We consider the detuning parameters and analyze the bifurcations.
©2020 American Institute of Physics
©2020 American Institute of Physics
MSC:
| 37J40 | Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion |
| 37J20 | Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems |
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