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Analytic Invariant Curves for a Planar Mapping

Analytic Invariant Curves for a Planar Mapping
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摘要 This paper is concerned with the existence of analytic invariant curves for a planar mapping. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained. In this paper, we discuss not only the general case, but also the critical cases as well, in particular, the case where β is a unit root is discussed. This paper is concerned with the existence of analytic invariant curves for a planar mapping. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained. In this paper, we discuss not only the general case, but also the critical cases as well, in particular, the case where β is a unit root is discussed.
作者 Wen Rong LI Han Ze LIU Li YIN
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第4期623-630,共8页 数学学报（英文版）
关键词 planar mapping invariant curves analytic solution Majorant series planar mapping, invariant curves, analytic solution, Majorant series
分类号 O186 [理学—基础数学]
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参考文献16

  • 1Moser, J.: On invariant curves of area-preserving maps of an annulus. Nachr. Akad. Wiss. Gottingen, 1, (1962)
  • 2Kuczma, M.: Functional Equations in a Single Variable, Polish Scientific, Warszawa, 1968
  • 3Diamond, P. M.: Analytic invariants of mappings of two variables. J. Math. Anal. Appl., 27, 601-608 (1969)
  • 4Kuczma, M., Choczewski, B., Ger, R.:Iterative Functional Equations, Encycl. Math. Appl., 32, Cambridge University Press, Cambridge, 1990
  • 5Jarczyk, W.: On continuous solutions of the equation of invariant curves, Constantin Caratheodory; An International Tribute, Vol. 1, World Scientific, Teaneck, 1991, 527-542
  • 6Ng, C. T., Zhang, W.: Invariant curves for a planar mapping. J. Differ. Equations Appl., 3, 147-168 (1997)
  • 7Si, J. G., Zhang, W. N.: Analytic solutions of a functional equation for invariant curves. J. Math. Anal. Appl., 259, 83-93 (2001)
  • 8Si, J. G., Zhaag, W. N.: Analytic solutions of a nonlinear iterative equation near neutral fixed point and poles. J. Math. Anal. Appl., 284, 373-388 (2003)
  • 9Si, J. G., Zhang, W. N.: Analytic solutions of a second-order non-autonomous iterative functional differential equation. J. Math. Anal. Appl., 306, 398-412 (2005)
  • 10Petropoulou, E. N., Siafarikas, P. D.- Existence and Uniqueness of solutions in H1(Δ) of a general class of non-linear functional equations. J. Math. Anal. Appl., 279, 451-462 (2003)
Acta Mathematica Sinica,English Series
2008年 第4期

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