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周期系统Laurent多项式型首次积分的不存在性 被引量：2

Nonexistence of Laurent Polynomial First Integrals for Periodic Systems
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摘要 考虑周期系统Laurent多项式型首次积分的不存在性.利用Floquet理论,证明了如果系统的特征乘数是-非共振的,则系统在平衡点附近不存在Laurent多项式型首次积分. We considered the nonexistence of Laurent polynomial first integrals for periodic system. Using the Floquet theory, we have proved that if the characteristic multipliers of the system are Z-independent, then the system does not have any nontrivial Laurent first integral in a neighborhood of a constant solution.
作者 焦佳 付苗苗 马勇
机构地区 吉林大学数学研究所 长春师范学院数学系 吉林大学数学学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2009年第1期44-47,共4页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:J0630104)
关键词 Laurent多项式 首次积分 FLOQUET理论 Laurent polynomial first integral Floquet theory
分类号 O175 [理学—基础数学]
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参考文献9

  • 1Poincare H. Sur I' integrations des Equations Differentielles du Premier Order et du Premier Degre Ⅰ and Ⅱ Rend [J]. Circolo Mat Palermo, 1891, 11: 193-239.
  • 2Yoshida H. Necessary Condition for the Existence of Algebraic First Integrals Ⅰ,Ⅱ[ J ]. Celestial Mech Dynamical Astronomy, 1983, 31(4): 363-379; 381-399.
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同被引文献22

  • 1POINCARE H. Sur I 'integrations des equations fifferentielles du premier order et dupremier degre Ⅰ and Ⅱ Rend [J]. Circolo Mat Palermo, 1891, 11 : 193 - 239.
  • 2YOSHIDA H. Necessary condition for the non -exist- ence of algebraic first integral ( Ⅰ, Ⅱ ) [ J ]. Celestial Mech, 1983, 31:363-379, 381-399.
  • 3KOWALEVSKI S. Sur le probleme de la rotation d 'un corps solide autour d'un point fixe [ J ]. Acta Math. , 1889, 12:177-232.
  • 4KUMMER M, CHURCHILL R C, ROD D L. On Kova- levski expoenents [J]. Can. Math. Bull. , 1990, 33:175 -180.
  • 5GORIELY A. Integrability, partial integrability, and nonintegrability for systems of ordinary differential e- quations [J]. J. Math. Phys., 1996, 37:1871 - 1993.
  • 6SADETOV S T. On resonances of the Kovalevskaya ex- ponents [J]. Math. Notes, 1993, 54:1081-1083.
  • 7FURTA S D. On non - integrability of general systems of differential equations [ J]. Z Angew Math Phys, 1996, 47:112-31.
  • 8NOWICKI A. On the nonexistence of rational first inte- grals for systems of linear differential equations [ J ]. Linear Algebra Appl, 1996, 235: 107- 120.
  • 9SHI Shaoyun, LI Yong. Non -integrability for general nonlinear systems [ J ]. Z Angew Math Phys, 2001, 52:191-200.
  • 10SHI Shaoyun. On the nonexistence of rational first inte- grals for nonlinear systems and semiquasihomogeneous systems [J]. J. Math. Anal. Appl. , 2007, 335:125 - 134.

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吉林大学学报（理学版）
2009年 第1期

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