“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 17559 |
|
| Abstract: | |
|
The 1:2:3 Hamiltonian resonance is one of the four genuine first order resonances which is non-integrable. For this resonance, chaotic behavior of the normal form has been shown due to the existence of a transverse homoclinic orbit on the energy manifold. Considering the detuning parameters, in the mirror symmetric cases of the Poisson manifold, by a reduction theory and computing the classical normal form of non-degenerate Hamiltonian Hopf bifurcation, we show there are just non-degenerate Hamiltonian Hopf bifurcations. However in the general case by considering some case studies and specially of FPU (FermiâPastaâUlam) chains for a fiber passaging 1:2:3 resonance, we may deal with complex dynamics and specially Hamiltonian Hopf bifurcation in a complicated region. Actually, we can see some special Krein collisions in a complex region.
Download TeX format |
|
| back to top | |
