Non-trivial wandering domains for heterodimensional cycles
Non-trivial wandering domains for heterodimensional cycles
复制标题
异维循环的非平凡漫游域
DOI：
10.1088/1361-6544/aa7cc6
复制
发表时间：
2017
期刊：
影响因子：
1.7
通讯作者：
Teruhiko Soma
中科院分区：
文献类型：
--
作者：
Shin Kiriki;Yushi Nakano ;Teruhiko Soma
本文给出了具有异维环的三维微分同态可以被具有非平凡收缩漫游域的微分同态通过若干扰动任意逼近的充分条件。本文的主要思想是证明具有非实特征值鞍点的异维环的微分同态可以用Tatjer提出的具有广义同斜切线的微分同态来近似。广义同斜切线是一个包含Bogdanov-Takens分岔的组织中心，通过它可以获得非平凡的收缩漫游域和Denjoy-like结构。
We present a sufficient condition for three-dimensional diffeomorphisms having heterodimensional cycles to be approximated arbitrarily well by diffeomorphisms with non-trivial contracting wandering domains via several perturbations. The key idea is to show that diffeomorphisms with heterodimensional cycles associated with saddle points with non-real eigenvalues can be approximated by diffeomorphisms with generalized homoclinic tangencies presented by Tatjer. The generalized homoclinic tangency is an organizing center including a Bogdanov–Takens bifurcation, by which one can obtain non-trivial contracting wandering domains together with a Denjoy-like construction.