On the Detuned 2:4 Resonance

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Detuned 2:4 Resonance

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the Detuned 2:4 Resonance

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA17-11805S" target="_blank" >GA17-11805S: Superintegrabilní systémy v magnetických polích ve třech prostorových rozměrech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of nonlinear science

ISSN

0938-8974

e-ISSN

1432-1467

Svazek periodika

30

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

32

Strana od-do

2513-2544

Kód UT WoS článku

000533816400001

EID výsledku v databázi Scopus

2-s2.0-85085165578