一类差分方程的不变曲线分枝

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基金项目: 云南省自然科学基金资助(1999A0018M)

Bifurcations of Invariant Curves of a Difference Equation

Institute of Science, Kunming University of Science and Technology, Kunming 650093, P R China

摘要: 讨论一类差分方程的不变曲线分枝。由于该差分方程所定义的动力系统是可积的,故该方程的不变曲线的讨论可化为对平面Hamilton系统所定义的轨线的拓扑分类的研究。通过严格的定性分析,获得其不变曲线在参数空间内的分类。
- 差分方程 /
- Hamilton系统 /
- 不变曲线
Abstract: Bifurcation of the invariant curves of a difference equationis studied. The system defined by the difference equation is integrable, sothe study of the invariant curves of the difference system canbecome the study of topological classification of the planar phase portraits defined by a planar Hamiltonia system. By strict qualitative analysis, the classification of the invariant curves in parameter space can be obtained.
- difference equation /
- Hamiltonian system /
- invariant curve

[1]	Sahadevan R. On invariants for difference equations and systems of difference equations of rational form[J]. J Math Anal Appl,1999,233:498-507.
[2]	Schinas C J. Invariants for difference equation and systems of difference equation of rational form[J]. J Math Anal Appl,1997,216:164-179.
[3]	Veselov A P. Integrable maps[J]. Russian Math Survey,1991,46(5):1-52.
[4]	LI Ji-bin,LIU Zheng-rong. Invariant curves of the generalized Lyness equation[J]. Int J Bifurcation and Chaos,1999,9(7):1143-1450.
[5]	张芷芬,等. 微分方程定性理论(现代数学丛书)[M]. 北京:科学出版社,1985.
[6]	李继彬,冯贝叶. 稳定性分支与混沌[M]. 昆明:云南科技出版社,1994.
[7]	李继彬,李存富. 非线性微分方程[M]. 成都:成都科技大学出版社,1987.