一个庞卡莱映射的逼近

(厦门大学数学科学学院,福建 厦门 361005)

庞卡莱映射; 同宿轨; 一致逼近

Approximations of a Poincaré Map
JIA Lukun,CHENG Jinfa*,WEN Yongming

(School of Mathematical Sciences,Xiamen University,Xiamen 361005,China)

Poincaré; map; homoclinic orbit; linearly approximated

DOI: 10.6043/j.issn.0438-0479.201601028

备注

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.

We can construct a Poincaré 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 Poincaré map can be approximated linearly in its whole domain.In the end,using our method we get a subset in which the Poincaré map can be linearly approximated.