Perturbations of quadratic centers
نویسندگان
چکیده
منابع مشابه
Quadratic perturbations of quadratic codimension-four centers
We study the stratum in the set of all quadratic differential systems ẋ = P2(x, y), ẏ = Q2(x, y) with a center, known as the codimension-four case Q4. It has a center and a node and a rational first integral. The limit cycles under small quadratic perturbations in the system are determined by the zeros of the first Poincaré-Pontryagin-Melnikov integral I. We show that the orbits of the unpertur...
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The problem of minimizing f̃ = f +p over some convex subset of a Euclidean space is investigated, where f(x) = x Ax + b x is a strictly convex quadratic function and |p| is only assumed to be bounded by some positive number s. It is shown that the function f̃ is strictly outer γ-convex for any γ > γ∗, where γ∗ is determined by s and the smallest eigenvalue of A. As consequence, a γ∗-local minimal...
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ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 1998
ISSN: 0007-4497
DOI: 10.1016/s0007-4497(98)80080-8