向量丛动力系统研究註记(Ⅱ)──部份1
Notes on a Study of Vector Bundle Dynamical Systems(Ⅱ)──Part1
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摘要: 过去,向量丛线性动力系统的整体线性性质研究已经显得相当广泛。现在,我们提议研究这种线性系统的扰动性质。我们要考虑的这种扰动系统将不再是线性的,但要研究的性质一般仍是整体性的。再者我们感兴趣的为非一致双曲性。在本文中我们给出了这种扰动的恰当的定义。它虽表现得有几分不太通常,然而它较深地植根于有关微分动力系统理论的典泛方程组中。这里一般的问题是要观察,当扰动发生后,原给系统的何种性质得以保持下来。本文的全部内容是要建立这种类型的一个定理。Abstract: The study of linear and global.properties of linear dynamical systems on vector bundles appeared rather extensive already in the past.Presently we propose to study perturbations of this linear dynamics The perturbed dynamical system which we shallconsider is no longer linear.while the properties to be studied will be still global in general.Moreover.we are interested in the nonuniformly hyperbolic properties.In this paper,we set an appropriate definition for such perturbations.Though it appears somewhat not quite usual yet has deeper root in standard systens of differential equations in the theory of differentiable dynamical systens The general problen is to see which property of the original given by the dynamical system is persistent when a perturbation takes place.The whole contenl of the paper is deyoted to establishing a theorem of this sort.
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