Bifurcation Sequences in the Symmetric 1:1 Hamiltonian Resonance
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Bifurcation Sequences in the Symmetric 1:1 Hamiltonian Resonance
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/EE2.3.30.0034" target="_blank" >EE2.3.30.0034: Support of inter-sectoral mobility and quality enhancement of research teams at Czech Technical University in Prague</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Bifurcations and Chaos
ISSN
0218-1274
e-ISSN
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Volume of the periodical
26
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
32
Pages from-to
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UT code for WoS article
000375388700003
EID of the result in the Scopus database
2-s2.0-84966570206