某类常微系统的一个基本性质

<正> 简介 考虑一n维紧致的C~∞型Riemann流形M~n(n≥2)上,由所有的C~1型常微系统就C~1度量作成的空间.这里为简便,一系统∈将暂称为A_o-系统,如果它只具有有限多个奇点和至多可数多个周期轨道;将暂称为A_1-系统,如果它只具有有限多个奇点和有限多个周期轨道.依据周知的结果,一般绝不是中每一系统都有任意小的邻

A BASIC PROPERTY OF A CERTAIN CLASS OF DIFFERENTIAL SYSTEMS

Let M~n be a compact C~∞ Riemann manifold of dimension n 2. Consider an arbitrarily given C~1 differential system S on M~n. Then S induces a C~1 one-parame-ter transformation group φ_t:M~n→M~n (-∞0 and T>0 such that It is also easily seen that, when S ∈The result which we obtain is the following theorem. It is the basic property of, as mentioned in the title.Theorem. There exists an open covering of, and corresponding to each H∈there exist numbcrs η_H>0 and T_H>0 sueh that: if V∈and S∈V, then Whenever a point on a peridic orbit of S and T_v≤t<∞, we haveWhenever is a periodic orbit of S with period To, x∈P,and 0=to