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Title:
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Periodic motion in perturbed elliptic oscillators revisited
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Author:
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Corbera Subirana, Montserrat; Llibre, Jaume; Valls, C.
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Other authors:
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Universitat de Vic - Universitat Central de Catalunya. Facultat de Ciències i Tecnologia |
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Notes:
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We analytically study the Hamiltonian system in
R4 with Hamiltonian
H = 1
2
p2
x
+p2
y + 1
2
ω2
1x2 +ω2
2y2 − εV (x, y)
being V (x, y) = −(x2y + ax3) with a ∈ R, where ε is a
small parameter and ω1 and ω2 are the unperturbed frequencies
of the oscillations along the x and y axis, respectively.
Using averaging theory of first and second order we analytically
find seven families of periodic solutions in every
positive energy level of H when the frequencies are not
equal. Four of these seven families are defined for all a ∈ R
whereas the other three are defined for all a = 0. Moreover,
we provide the shape of all these families of periodic solutions.
These Hamiltonians may represent the central parts of
deformed galaxies and thus have been extensively used and
studied mainly numerically in order to describe local motion
in galaxies near an equilibrium point. |
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Subject(s):
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-Estels binaris |
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Rights:
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Tots els drets reservats
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Document type:
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Article
info:eu-repo/acceptedVersion |
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Published by:
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Springer Verlag
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Share:
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