On stability at the Hamiltonian Hopf Bifurcation
โ Scribed by L. M. Lerman; A. P. Markova
- Book ID
- 111469494
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 2009
- Tongue
- English
- Weight
- 586 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1560-3547
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๐ SIMILAR VOLUMES
The Hamiltonian Hopf bifurcation has an integrable normal form that describes the passage of the eigenvalues of an equilibrium through the 1 : -1 resonance. At the bifurcation the pure imaginary eigenvalues of the elliptic equilibrium turn into a complex quadruplet of eigenvalues and the equilibrium
We consider the hydrogen atom in crossed electric and magnetic fields. We prove that near the Stark and Zeeman limits the system goes through two qualitatively different Hamiltonian Hopf bifurcations. We explain in detail the geometry of the bifurcations.