منابع مشابه
Stable Piecewise Polynomial Vector Fields
Let N = {y > 0} and S = {y < 0} be the semi-planes of R2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise polynomial vector field Z = (X, Y ). This work pursues the stability and the transition analysis of solutions of Z between N and S, started by Filippov (1988) and Kozlova (1984) and...
متن کاملCommuting Planar Polynomial Vector Fields for Conservative Newton Systems
We study the problem of characterizing polynomial vector fields that commute with a given polynomial vector field on a plane. It is a classical result that one can write down solution formulas for an ODE that corresponds to a planar vector field that possesses a linearly independent commuting vector field. This problem is also central to the question of linearizability of vector fields. Let f ∈...
متن کامل08w5055 Classical Problems on Planar Polynomial Vector Fields
At the end of the 19th century Poincaré and Hilbert stated three problems which are still open today: the problem of the center and the problem of Poincaré, stated by Poincaré in 1885 and in 1891, and Hilbert’s 16th problem, stated in Hilbert’s address at the International Congress of Mathematicians in Paris in 1900. The first two and the second part of Hilbert’s 16th problem are on planar poly...
متن کاملHilbert's 16th Problem and bifurcations of Planar Polynomial Vector Fields
The original Hilbert’s 16th problem can be split into four parts consisting of Problems A–D. In this paper, the progress of study on Hilbert’s 16th problem is presented, and the relationship between Hilbert’s 16th problem and bifurcations of planar vector fields is discussed. The material is presented in eight sections. Section 1: Introduction: what is Hilbert’s 16th problem? Section 2: The fir...
متن کاملPlanar polynomial vector fields having a polynomial first integral can be obtained from linear systems
We consider in this work planar polynomial differential systems having a polynomial first integral. We prove that these systems can be obtained from a linear system through a polynomial change of variables.
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: Revista Matemática Iberoamericana
سال: 1985
ISSN: 0213-2230
DOI: 10.4171/rmi/8