On the centers of the weight-homogeneous polynomial vector fields on the plane
英文摘要：
We classify all the centers of a planar weight-homogeneous polynomial vector field of weight degree 1, 2, 3 and 4.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
Center-focus determination and limit cycles bifurcation for $p:q$ homogeneous weight singular point
The quasi-homogeneous (and in general non-homogeneous) polynomial differential systems have been studied from many different points of view. In this paper, Center-focus determination and limit cycles bifurcation for $p:q$ homogeneous weight singular point are investigated. Some prosperities of Successive function and focus values are discussed, furthermore, the method of computing focal values is given. As an example, center-focus determination and limit cycle bifurcation for $2:3$ homogeneous weight singular point are studied, three or five limit cycles in the neighborhood of origin can be ob…
math.DS
On the cyclicity of weight-homogeneous centers
Let W be a weight-homogeneous planar polynomial differential system with a center. We find an upper bound of the number of limit cycles which bifurcate from the period annulus of W under a generic polynomial perturbation. We apply this result to a particular family of planar polynomial systems having a nilpotent center without meromorphic first integral.
math.DS
拟齐次多项式平面系统的中心
Centers of quasi-homogeneous polynomial planar systems
本文确定了0至4次拟齐次多项式平面向量场的中心，研究了各中心的可逆性与解析可积性，并发现了既非轨道可逆也非解析可积的多项式中心这一新场景。
math.DS
Global dynamics and unfolding of planar piecewise smooth quadratic quasi-homogeneous differential systems
In this paper we research global dynamics and bifurcations of planar piecewise smooth quadratic quasi--homogeneous but non-homogeneous polynomial differential systems. We present sufficient and necessary conditions for the existence of a center in piecewise smooth quadratic quasi--homogeneous systems. Moreover, the center is global and non-isochronous if it exists, which cannot appear in smooth quadratic quasi-homogeneous systems. Then the global structures of piecewise smooth quadratic quasi--homogeneous but non-homogeneous systems are studied. Finally we investigate limit cycle bifurcations …
math.DS
齐性空间上微分正系统的伯克霍夫中心与循环行为
Birkhoff center and recurrent behavior of differentially positive systems on a homogeneous space
School of Mathematics and Physics, University of Science and Technology Beijing（北京科技大学数学与物理学院）；School of Mathematical Sciences, University of Science and Technology of China（中国科学技术大学数学科学学院）；Department of Mathematical and Statistical Sciences, University of Alberta（阿尔伯塔大学数学与统计科学系）
本文研究齐性空间上微分正系统的伯克霍夫中心结构与循环行为，建立其序结构二分性，完成循环动力学的完整刻画。
math.DS
非光滑扰动下从权次数2的拟齐次多项式中心分岔出的极限环
Limit cycles bifurcating from the quasi-homogeneous polynomial centers of weight-degree 2 under non-smooth perturbations
研究三次多项式微分中心在三次分段光滑多项式扰动下的极限环最大数量，利用一阶平均法获得切换线为$x=0$或$y=0$时的精确界，揭示非光滑系统比光滑系统拥有更多极限环。
math.DS
更多相关论文收起更多论文
Planar Semi-quasi Homogeneous Polynomial differential systems with a given degree
This paper study the planar semi-quasi homogeneous polynomial differential systems (short for PSQHPDS), which can be regard as a generalization of semi-homogeneous and of quasi-homogeneous systems. By using the algebraic skills, several important properties of PSQHPDS are derived and are employed to establish an algorithm for obtaining all the explicit expressions of PSQHPDS with a given degree. Afterward, we apply this algorithm to research the center problem of quadratic and cubic PSQHPDS. It is proved that the quadratic one hasn't center, and, that the cubic one has center if and only if it…
math.DS
具有齐次非线性项的分段哈密顿微分系统的非等时性
Non-isochronicity on piecewise Hamiltonian differential systems with homogeneous nonlinearities
本文针对具有直线切换线和齐次非线性哈密顿子系统的平面分段光滑微分系统，证明了其Σ-中心的非等时性。
math.DS
具有齐次非线性项的等变微分方程的单调周期函数
Monotonous period function for equivariant differential equations with homogeneous nonlinearities
本文证明了 $\mathbb{Z}_k$-等变微分方程 $\dot{z}=iz+a(z\overline{z})^nz^{k+1}$ 在原点的中心的周期函数对所有正整数 $n,k$ 均单调递减，并作为可逆二次中心子族周期函数单调性的推论，解决了相关猜想。
math.DS
On the polynomials homogeneous ergodic bilinear averages with Liouville and Möbius weights
We establish a generalization of Bourgain double recurrence theorem by proving that for any map $T$ acting on a probability space $(X,\mathcal{A},μ)$, and for any non-constant polynomials $P, Q$ mapping natural numbers to themselves, for any $f,g \in L^2(X)$, and for almost all $x \in X$, we have $$\lim_{\bar{N} \longrightarrow +\infty} \frac{1}{N} \sum_{n=1}^{N}\boldsymbolν(n) f(T^{P(n)}x)g(T^{Q(n)}x)=0$$ where $\boldsymbolν$ is the Liouville function or the Möbius¶ function.
math.DS
Kovalevskaya exponents and the space of initial conditions of a quasi-homogeneous vector field
Formal series solutions and the Kovalevskaya exponents of a quasi-homogeneous polynomial system of differential equations are studied by means of a weighted projective space and dynamical systems theory. A necessary and sufficient condition for the series solution to be a convergent Laurent series is given, which improve the well known Painlevé test. In particular, if a given system has the Painlevé property, an algorithm to construct Okamoto's space of initial conditions is given. The space of initial conditions is obtained by weighted blow-ups of the weighted projective space, where the weig…
math.CAmath.DS
关于拟齐次多项式向量场的周期环域的循环性
On the cyclicity of the period annulus of quasi-homogeneous polynomial vector fields
University of Toulouse（图卢兹大学）
研究在单参数多项式扰动下，具有中心的拟齐次多项式向量场从周期环域分岔出的极限环个数，通过改进的Francoise算法和组合技术建立了k阶Melnikov函数孤立零点数的上界公式。
math.CAmath.DS
