On the Detuned 2:4 Resonance
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F20%3A00343790" target="_blank" >RIV/68407700:21240/20:00343790 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00332-020-09628-7" target="_blank" >https://doi.org/10.1007/s00332-020-09628-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00332-020-09628-7" target="_blank" >10.1007/s00332-020-09628-7</a>
Alternative languages
Result language
angličtina
Original language name
On the Detuned 2:4 Resonance
Original language description
We consider families of Hamiltonian systems in two degrees of freedom with an equilibrium in 1 : 2 resonance. Under detuning, this "Fermi resonance" typically leads to normal modes losing their stability through period-doubling bifurcations. For cubic potentials, this concerns the short axial orbits, and in galactic dynamics, the resulting stable periodic orbits are called "banana" orbits. Galactic potentials are symmetric with respect to the coordinate planes whence the potential-and the normal form-both have no cubic terms. This Z2xZ2 symmetry turns the 1 : 2 resonance into a higher-order resonance, and one therefore also speaks of the 2 : 4 resonance. In this paper, we study the 2 : 4 resonance in its own right, not restricted to natural Hamiltonian systems where H=T+V would consist of kinetic and (positional) potential energy. The short axial orbit then turns out to be dynamically stable everywhere except at a simultaneous bifurcation of banana and "anti-banana" orbits, while it is now the long axial orbit that loses and regains stability through two successive period-doubling bifurcations.
Czech name
—
Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA17-11805S" target="_blank" >GA17-11805S: Superintegrable systems in magnetic fields in three spatial dimensions</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of nonlinear science
ISSN
0938-8974
e-ISSN
1432-1467
Volume of the periodical
30
Issue of the periodical within the volume
6
Country of publishing house
CH - SWITZERLAND
Number of pages
32
Pages from-to
2513-2544
UT code for WoS article
000533816400001
EID of the result in the Scopus database
2-s2.0-85085165578