|
|
|
题名
|
作者
|
年代
|
出处
|
被引量
|
| 1 | INTEGRABILITY VIA INVARIANT ALGEBRAIC CURVES FOR PLANAR POLYNOMIALDIFFERENTIAL SYSTEMS显示文摘We present an introduction to the Darboux integrability theory of planar complex and real polynomial differential systems containing some improvements to the classical theory. | Colin Christopher (School of Mathematics and Statistics, University of Plymouth, Plymouth, Devon PL4 SAA, UNITED KINGDOM) Jaume Llibre (Dopartament de Matematiques, Universitat Autonoma de Barcelona, 08193-Bellaterra, Barcelona, SPAIN) | 2000 | Annals of Differential Equations2000，16，1： | 4 |
| 2 | NEW FAMILIES OF CENTERS AND LIMIT CYCLES FOR POLYNOMIAL DIFFERENTIAL SYSTEMS WITH HOMOGENEOUS NONLINEARITIES显示文摘We consider the class of polynomial differential equations x = -y+Pn(x,y), y = x + Qn(x, y), where Pn and Qn are homogeneous polynomials of degree n. Inside this class we identify a new subclass of systems having a center at the origin. We show that this subclass contains at least two subfamilies of isochro-nous centers. By using a method different from the classical ones, we study the limit cycles that bifurcate from the periodic orbits of such centers when we perturb them inside the class of all polynomial differential systems of the above form. In particular, we present a function whose simple zeros correspond to the limit cycles vvhich bifurcate from the periodic orbits of Hamiltonian systems. | 李承治 李伟固 Jaume Llibre 张芷芬 | 2003 | Annals of Differential Equations2003，19，3： | 2 |
| 3 | Liouvillian and Analytic Integrability of the Quadratic Vector Fields Having an Invariant Ellipse显示文摘We characterize the Liouvillian and analytic integrability of the quadratic polynomial vector fields in R2 having an invariant ellipse.More precisely,a quadratic system having an invariant ellipse can be written into the form x=x2+y2-1+y(ax+by+c),y=x(ax+by+c),and the ellipse becomes x2+y2=1.We prove that(i) this quadratic system is analytic integrable if and only if a=0;(ii) if x2+y2=1 is a periodic orbit,then this quadratic system is Liouvillian integrable if and only if x2+y2=1 is not a limit cycle;and(iii) if x2+y2=1 is not a periodic orbit,then this quadratic system is Liouvilian integrable if and only if a=0. | Jaume LLIBRE Claudia VALLS | 2014 | Acta Mathematica Sinica,English Series2014，30，3： | 2 |
| 4 | New central configurations for the planar 5-body problem 显示文摘 | Jaume Llibre Luis Fernando Mello | 2008 | Celestial Mech Dyn Astr2008，100，： | 1 |
| 5 | New doubly- symmetric families of comet-like periodic orbits in the spatial restricted ( N + 1 )-body problem 显示文摘 | Jaume Llibre Luci Any Roberto | 2009 | Celest Mech Dyn Astr2009，104，： | 1 |
| 6 | New doubly- symmetric families of comet-like periodic orbits in the spatial restricted ( N q- 1 )-body problem 显示文摘 | Jaume Llibre Luci Any Roberto | 2009 | CelestMech Dyn Astr2009，104，： | 1 |
| 7 | New central configurations for the planar5-body problem显示文摘 | Jaume Llibre Luis Fernando Mello | | 0，，： | 1 |
| 8 | Symmetric planar central configurations of five bodies:Euler plus two显示文摘 | Marian Gidea Jaume Llibre | | 0，，： | 1 |
| 9 | 一类pitchfork分支的全局相图显示文摘本文研究二次微分系统dt/dr=y^2?y?x,dy/dt=x^2?μx?y,其中μ∈R.该系统是刻画pitchfork分支的重要例子.本文给出该系统在Poincare圆盘上的全局相图。 | 李时敏 Jaume Llibre | 2019 | 中国科学:数学2019，49，9： | 1 |
| 10 | Polynomial systems: A lower bound for the weakened 16th Hilbert problem显示文摘 | Li Chengzhi Li Weigu Llibre Jaume | 2001 | Extracta Math2001，16，3： | 1 |
| 11 | New doubly-symmetric families of comet-like periodic orbits in the spatial restricted(N + 1 )-body problem显示文摘 | Jaume Llibre Luci Any Roberto | | 0，，： | 1 |
| 12 | Limit Cycles for a Mechanical System Coming from the Perturbation of a Four–Dimensional Linear Center显示文摘 | Jaume Llibre Marco Antonio Teixeira | 2006 | Journal of Dynamics and Differential Equations2006，，4： | 1 |
| 13 | Averaging methods for finding periodic orbits via Brouwer degree显示文摘 | Adriana Buic? Jaume Llibre | 2003 | Bulletin des sciences mathematiques2003，，1： | 1 |
| 14 | New stacked central configurations for theplanar 5-body problem显示文摘 | Jaume Llibre Luis Fernando Mello Ernesto Perez-Chavela | | 0，，： | 1 |
| 15 | On the periodic orbit bifurcating from a zero Hopf bifurcation in systems with two slow and one fast variables显示文摘 | Isaac A. García Jaume Llibre Susanna Maza | 2014 | Applied Mathematics and Computation2014，，： | 1 |
| 16 | Periods for triangular maps显示文摘 | LLUíS ALSEDà JAUME LLIBRE | 1993 | Bull Austral Math Soc1993，47，： | 1 |
| 17 | 具有全局中心的平面多项式Hamilton系统显示文摘本文给出平面多项式Hamilton系统具有全局中心的充要条件,这刻画出整个实平面有叶层结构,即它被该系统对应的多项式Hamilton函数的水平集(即实代数曲线)分层,而每一层对应的实代数曲线都是卵形线(即紧闭分枝).进一步地,本文证明,对于任意正整数n和任意一种类型中心(即线性型、幂零型和退化型),都存在2n+1次平面多项式Hamilton系统使其具有该类型的全局中心,而2n次平面多项式Hamilton系统没有全局中心.作为特殊情形,本文也给出平面三次多项式Hamilton系统具有退化型中心的充要条件. | 何鸿锦 Jaume Llibre 肖冬梅 | 2022 | 中国科学:数学2022，52，6： | 1 |
| 18 | New central configurations for the planar 5-body problem 显示文摘 | Jaume Llibre Luis Fernando Mello | 2008 | Celestial Mech Dyn Astr2008，100，： | 1 |
| 19 | Limit cycles for a class of second order differential equations显示文摘 | Jaume Llibre Ernesto Perez-Chavela | 2011 | Physics Letters A2011，，7： | 1 |
| 20 | Averaging methods for finding periodic orbits via Brouwer degree显示文摘 | Adriana Buic? Jaume Llibre | 2003 | Bulletin des sciences mathematiques2003，，1： | 1 |
您所在的机构暂未开通此部分的功能，请联系管理员