映射與向量場之關聯

Abstract

我們對於由Takens's lemma所做出來的向量場和原來的映射感興趣。特別是，對於有對稱性的映射我們更感興趣，如：symplectic映射或（和）reversible映射。我們利用Wan的方法來建立MacMillan類的映射之相對應的向量場。利用數值上的模擬來研究向量場附近的週期軌跡以及映射的週期點。

We are interested in the relationship between a map and the vector field corresponding to it obtained from Takens's lemma. More specifically, we are interested in the symmetric maps such as symplectic or (and) reversible maps. We use the method of the product normal form to construct the corresponding vector fields for the so-called McMillan class of area-preserving maps. Numerical simulation are performed to study the periodic orbits of the vector fields near fixed points and the periodic points of the maps.