Bifurcation Sequences in the Symmetric 1:1 Hamiltonian Resonance

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F16%3A00301978" target="_blank" >RIV/68407700:21340/16:00301978 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1142/S0218127416300111" target="_blank" >http://dx.doi.org/10.1142/S0218127416300111</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218127416300111" target="_blank" >10.1142/S0218127416300111</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Bifurcation Sequences in the Symmetric 1:1 Hamiltonian Resonance

Popis výsledku v původním jazyce

We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under Z(2) x Z(2) symmetry. The rich structure of these classical systems is investigated with geometric methods and the relation with the singularity theory approach is also highlighted. The geometric approach is the most straightforward way to obtain a general picture of the phase-space dynamics of the family as is defined by a complete subset in the space of control parameters complying with the symmetry constraint. It is shown how to find an energy-momentum map describing the phase-space structure of each member of the family, a catastrophe map that captures its global features and formal expressions for action- angle variables. Several examples, mainly taken from astrodynamics, are used as applications.

Název v anglickém jazyce

Bifurcation Sequences in the Symmetric 1:1 Hamiltonian Resonance

Popis výsledku anglicky

We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under Z(2) x Z(2) symmetry. The rich structure of these classical systems is investigated with geometric methods and the relation with the singularity theory approach is also highlighted. The geometric approach is the most straightforward way to obtain a general picture of the phase-space dynamics of the family as is defined by a complete subset in the space of control parameters complying with the symmetry constraint. It is shown how to find an energy-momentum map describing the phase-space structure of each member of the family, a catastrophe map that captures its global features and formal expressions for action- angle variables. Several examples, mainly taken from astrodynamics, are used as applications.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/EE2.3.30.0034" target="_blank" >EE2.3.30.0034: Podpora zkvalitnění týmů výzkumu a vývoje a rozvoj intersektorální mobility na ČVUT v Praze</a><br>

Návaznosti

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

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

International Journal of Bifurcations and Chaos

ISSN

0218-1274

e-ISSN

—

Svazek periodika

26

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

32

Strana od-do

—

Kód UT WoS článku

000375388700003

EID výsledku v databázi Scopus

2-s2.0-84966570206