摘要
本文的主要目的是摘要叙述下面定理的一个证明。主要定理设M^(n)是一n维C^(∞)Riemann流形,n■2,其上有一C^(1)常微系统S.命a是S的一非游荡常点。则对每一ε>0,M^(n)上有一C^(1)常微系统X具有一周期轨道经过a且满足‖X—S‖1<ε。这在微分动力体系理论中是一推广形式的封闭引理。
This note takes a sketch on a more conceptual proof of the following theorem.Theorem Let M^(n)be an n-dimensional C^(∞)Riemann manifold, n≥2, on which there is given a C^(1) differential system S. Let a be a non-wandering point of S. Then, for each ∈>0, there is a C^(1) differential system X on M^(n)which possesses a periodic orbit through a such that ‖X-S‖1<∈.When M^(n)is compact, this is the closing lemma of Pugh. A further similar result can also be obtained in case when the ω-limit set or the a-limit set of the orbit through a is non-empty.
出处
《科学通报》
1979年第19期865-868,共4页
Chinese Science Bulletin
