Limit Cycles Bifurcating from a Perturbed Quartic Center
نویسندگان
چکیده
We consider the quartic center ẋ = −yf(x, y), ẏ = xf(x, y), with f(x, y) = (x+a)(y+b)(x+c) and abc 6= 0. Here we study the maximum number σ of limit cycles which can bifurcate from the periodic orbits of this quartic center when we perturb it inside the class of polynomial vector fields of degree n, using the averaging theory of first order. We prove that 4[(n− 1)/2] + 4 ≤ σ ≤ 5[(n− 1)/2 + 14, where [η] denotes the integer part function of η.
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تاریخ انتشار 2015