Non-trivial wandering domains for heterodimensional cycles

被引:6
|
作者
Kiriki, Shin [1 ]
Nakano, Yushi [2 ]
Soma, Teruhiko [3 ]
机构
[1] Tokai Univ, Dept Math, 4-1-1 Kitakaname, Hiratsuka, Kanagawa 2591292, Japan
[2] Kitami Inst Technol, 165 Koen Cho, Kitami, Hokkaido 0908507, Japan
[3] Tokyo Metropolitan Univ, Dept Math & Informat Sci, Minami Ohsawa 1-1, Hachioji, Tokyo 1920397, Japan
关键词
heterodimensional cycle; Tatjer condition; wandering domain; Hopf bifurcation; homoclinic tangency; ONE-DIMENSIONAL DYNAMICS; TOPOLOGICAL ATTRACTORS; NEGATIVE SCHWARZIAN; DIFFEOMORPHISMS; TANGENCIES; INTERVALS; MAPS; NONEXISTENCE; BIFURCATION; SYSTEMS;
D O I
10.1088/1361-6544/aa7cc6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:3255 / 3270
页数:16
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