EXTENDING T-p AUTOMORPHISMS OVER Rp+2 AND REALIZING DE ATTRACTORS

作者：Ding Fan^*; Liu Yi; Wang Shicheng; Yao Jiangang

来源：Discrete and Continuous Dynamical Systems, 2012, 32(5): 1639-1655.

DOI：10.3934/dcds.2012.32.1639

• DE attractors
• extendable subgroup

We show that for every expanding self-map of a connected, closed p-dimensional manifold M, and for every codimension q >= p + 1, there exists a corresponding (p,q)-type DE attractor realized by a compactly-supported self-diffeomorphsm of Rp+q. Moreover, when M is the standard smooth p-dimensional torus T-p, the codimension q can be taken as two. As a key ingredient of the construction, for the standard unknotted embedding i(p) : T-p hooked right arrow Rp+2, we show the automorphisms that diffeomorphically extend over Rp+2 form a subgroup of Aut(T-p) of index at most 2(p) - 1.

• 出版日期2012-5
• 单位北京大学