Limit Cycle Bifurcations from an Order-3 Nilpotent Center of Cubic Hamiltonian Systems Perturbed by Cubic Polynomials
2020 ◽
Vol 30
(09)
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pp. 2050126
Keyword(s):
From [Han et al., 2009a] we know that the highest order of the nilpotent center of cubic Hamiltonian system is [Formula: see text]. In this paper, perturbing the Hamiltonian system which has a nilpotent center of order [Formula: see text] at the origin by cubic polynomials, we study the number of limit cycles of the corresponding cubic near-Hamiltonian systems near the origin. We prove that we can find seven and at most seven limit cycles near the origin by the first-order Melnikov function.
2012 ◽
Vol 22
(12)
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pp. 1250296
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2018 ◽
Vol 28
(03)
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pp. 1850038
2013 ◽
Vol 23
(03)
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pp. 1350043
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2015 ◽
Vol 25
(06)
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pp. 1550083
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Keyword(s):
Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop
2016 ◽
Vol 26
(12)
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pp. 1650204
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Keyword(s):
2016 ◽
Vol 26
(11)
◽
pp. 1650180
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2008 ◽
Vol 18
(10)
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pp. 3013-3027
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Keyword(s):
2020 ◽
Vol 30
(15)
◽
pp. 2050230
2017 ◽
Vol 27
(05)
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pp. 1750071
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Keyword(s):