中文摘要：

在连接同宿轨的双曲不动点附近可以构造一个庞卡莱映射，但一般来说，该庞卡莱映射及其线性逼近在其整个定义域内无法做到一致逼近．通过一个例子说明Wiggins S证明中的一个错误，给出庞卡莱映射在整个定义域内能被逼近的一个充分条件，并证明在庞卡莱映射定义域的一个子集内，该映射与其线性化映射可以做到一致逼近．

英文摘要：

We can construct a Poincare map near a hyperbolic point which joins a homoclinic orbit.But in general,it cannot be uni-formly approximated linearly in its whole domain.In this paper,we first show a claim in Stephen Wigginst proof is wrong by an ex-ample,and then give a sufficient condition under which the Poincare map can be approximated linearly in its whole domain. In theend,using our method we get a subset in which the Poincare map can be linearly approximated.