一个庞卡莱映射的逼近

Abstract

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Wig; gins; 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.

We can construct a Poincare map near a hyperbolic point which joins a; homoclinic orbit.But in general,it cannot be uniformly approximated; linearly in its whole domain.In this paper,we first show a claim in; Stephen Wiggins' proof is wrong by an example, and then give a; sufficient condition under which the Poincare map can be approximated; linearly in its whole domain. In the end, using our method we get a; subset in which the Poincare map can be linearly approximated.