Bounded Limit Cycles of Polynomial Foliations of $$\mathbb {C}^{2}$$ C 2
نویسندگان
چکیده
منابع مشابه
Polynomial Foliations of R 2
In 1940 Kaplan [14, 15] published two large papers on regular families of curves filling the plane, following previous ideas of Whitney [26]. A family of curves is called regular if it is locally homeomorphic with parallel lines. He proved that each curve of a regular family filling the plane is a homeomorphic line tending to infinity in both directions. A natural example of generating (orienta...
متن کاملOn polynomial approximations over $\mathbb{Z}/2^k\mathbb{Z}$
We study approximation of Boolean functions by low-degree polynomials over the ring Z/2kZ. More precisely, given a Boolean function F : {0, 1}n → {0, 1}, define its k-lift to be Fk : {0, 1}n → {0, 2k−1} by Fk(x) = 2k−F(x) (mod 2k). We consider the fractional agreement (which we refer to as γd,k(F)) of Fk with degree d polynomials from Z/2 Z[x1, . . . , xn]. Our results are the following: • Incr...
متن کاملLimit Cycles of a Class of Generalized Liénard Polynomial Equations
In this paper we study the maximum number of limit cycles of the following generalized Liénard polynomial differential system of the first order ẋ = y2p−1 ẏ = −x2q−1 − εf (x, y) where p and q are positive integers, ε is a small parameter and f (x, y) is a polynomial of degree m. We prove that this maximum number depends on p, q and m. AMS subject classification:
متن کاملThe number of limit cycles of a quintic polynomial system
In this paper we consider the bifurcation of limit cycles of the system ˙ x = y(x 2 − a 2)(y 2 − b 2) + εP(x, y), ˙ y = −x(x 2 − a 2)(y 2 − b 2) + εQ (x, y) for ε sufficiently small, where a, b ∈ R − {0}, and P, Q are polynomials of degree n, we obtain that up to first order in ε the upper bounds for the number of limit cycles that bifurcate from the period annulus of the quintic center given b...
متن کاملLimit Cycles of the Generalized Polynomial Liénard Differential Equations
We apply the averaging theory of first, second and third order to the class of generalized polynomial Liénard differential equations. Our main result shows that for any n, m ≥ 1 there are differential equations of the form ẍ+f(x)ẋ+g(x) = 0, with f and g polynomials of degree n and m respectively, having at least [(n + m− 1)/2] limit cycles, where [·] denotes the integer part function.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Brazilian Mathematical Society, New Series
سال: 2016
ISSN: 1678-7544,1678-7714
DOI: 10.1007/s00574-016-0005-9