ON THE NUMBER OF LIMIT CYCLES IN NEAR-HAMILTONIAN POLYNOMIAL SYSTEMS
2007 ◽
Vol 17
(06)
◽
pp. 2033-2047
◽
Keyword(s):
In this paper we study a general near-Hamiltonian polynomial system on the plane. We suppose the unperturbed system has a family of periodic orbits surrounding a center point and obtain some sufficient conditions to find the cyclicity of the perturbed system at the center or a periodic orbit. In particular, we prove that for almost all polynomial Hamiltonian systems the perturbed systems with polynomial perturbations of degree n have at most n(n + 1)/2 - 1 limit cycles near a center point. We also obtain some new results for Lienard systems by applying our main theorems.
1991 ◽
Vol 11
(1)
◽
pp. 65-71
◽
2021 ◽
Vol 31
(09)
◽
pp. 2150123
Keyword(s):
2008 ◽
Vol 18
(10)
◽
pp. 3013-3027
◽
Keyword(s):
2018 ◽
Vol 28
(02)
◽
pp. 1850026
2019 ◽
Vol 29
(12)
◽
pp. 1950160
2008 ◽
Vol 18
(07)
◽
pp. 1939-1955
◽
Keyword(s):
2020 ◽
Vol 30
(15)
◽
pp. 2050236
Keyword(s):
2015 ◽
Vol 25
(10)
◽
pp. 1550128
◽