Stabilization of heterodimensional cycles

被引:30
作者
Bonatti, C. [1 ]
Diaz, L. J. [2 ]
Kiriki, S. [3 ]
机构
[1] Inst Math Bourgogne, F-1078 Dijon, France
[2] PUC, Depto Matemat, BR-22453900 Rio De Janeiro, RJ, Brazil
[3] Kyoto Univ Educ, Dept Math, Fushimi Ku, Kyoto 6128522, Japan
关键词
HOMOCLINIC TANGENCIES; HYPERBOLICITY; DIFFEOMORPHISMS;
D O I
10.1088/0951-7715/25/4/931
中图分类号
O29 [应用数学];
学科分类号
070104 [应用数学];
摘要
We consider diffeomorphisms f with heteroclinic cycles associated with saddles P and Q of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to f with a robust cycle associated with hyperbolic sets containing the continuations of P and Q. We focus on the case where the indices of these two saddles differ by one. We prove that, excluding one particular case (so-called twisted cycles that additionally satisfy some geometrical restrictions), all such cycles can be stabilized.
引用
收藏
页码:931 / 960
页数:30
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