Higher Order Melnikov Functions for Studying Limit Cycles of Some Perturbed Elliptic Hamiltonian Vector Fields
Sign Up to like & getrecommendations! Published in 2019 at "Qualitative Theory of Dynamical Systems"
DOI: 10.1007/s12346-018-0284-1
Abstract: In this paper, we study the number of limit cycles in the perturbed Hamiltonian system $$dH=\varepsilon F_1+\varepsilon ^2 F_2+\varepsilon ^3 F_3$$dH=εF1+ε2F2+ε3F3 with $$F_i$$Fi, the vector valued homogeneous polynomials of degree i and $$4-i$$4-i for $$i=1,2,3$$i=1,2,3,… read more here.
Keywords: limit cycles; limit; higher order; melnikov functions ... See more keywords
Using Melnikov functions of any order for studying limit cycles
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DOI: 10.1016/j.jmaa.2016.11.021
Abstract: Abstract In this work we study a class of planar Hamiltonian systems perturbed with general quadratic polynomials in order to identify the number of limit cycles. Employing Melnikov functions of any order, we show that… read more here.
Keywords: order; limit cycles; melnikov functions; using melnikov ... See more keywords
Perturbed normalizers and Melnikov functions
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2018.04.004
Abstract: Abstract Given m ≥ 1 and a smooth family of planar vector fields ( X e ) e that is a perturbation of a period annulus, we provide a characterization, in terms of Lie brackets,… read more here.
Keywords: normalizers melnikov; perturbed normalizers; melnikov functions;