微分方程的拟解析解与o-极小结构
Quasianalytic solutions of differential equations and o-minimal structures
摘要：
众所周知，余维为1的实解析叶理的非螺旋叶都属于同一个o-极小结构。自然，如果同样的陈述对实解析向量场的非振荡轨线也成立，问题就来了。我们表明，在一定的假设下，这样的轨迹生成一个O-最小和模型完整的结构连同解析函数。证明使用的渐近理论的不规则奇异常微分方程，以建立一个准解析的结果，主要定理如下。作为应用，我们给出了一个无穷族的o-极小结构，使得任意两个o-极小结构都不允许公共扩张，并且我们构造了一个在实数的任何o-极小扩张中都不可定义的5维实解析向量场的非振荡轨线
英文摘要：
It is well known that the non-spiraling leaves of real analytic foliations of codimension 1 all belong to the same o-minimal structure. Naturally, the question arises if the same statement is true for non-oscillating trajectories of real analytic vector fields. We show, under certain assumptions, that such a trajectory generates an o-minimal and model complete structure together with the analytic functions. The proof uses the asymptotic theory of irregular singular ordinary differential equations in order to establish a quasi-analyticity result from which the main theorem follows. As applications, we present an infinite family of o-minimal structures such that any two of them do not admit a common extension, and we construct a non-oscillating trajectory of a real analytic vector field in dimension 5 that is not definable in any o-minimal extension of the reals
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