The ambient structure of expanding attractors I. Local triviality, tubular neighborhoods
The ambient structure of expanding attractors I. Local triviality, tubular neighborhoods
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DOI：
10.1002/mana.19821070126
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发表时间：
1982
影响因子：
1
通讯作者：
H. Bothe
中科院分区：
文献类型：
--
作者：
H. Bothe
1. 介绍。在动力学中，定义了一个光滑（即C-） m维流形的微分同态f: M-M， 31个吸引子（即com -1）作为/-不变的suI~(1)，它们吸引了所有接近1的点，在这种意义上，即极限力（f ' (p)）。-1)==（1持有）起中心作用。本质结构最容易理解的吸引子是膨胀吸引子，它的特征是存在一个实数a，使得f对a的限制限制了足够近的点之间的距离。(1) y的一个因子ri，（为了精确的定义）（+ Iichw）这些吸引子的拓扑结构是如何描述的？r . I =。\ lvmdrAm[7]。[$ 1, f9]。他证明了一个n维膨胀吸引子可以称为同胚于一个n维球与一个C~.\STOH的笛卡尔积。集，而全局结构的。I和f on的动力学。我可以用8个拓扑空间L‘来描述，它就像一个n流形，具有一定的t) ranch] mint和一个扩展映射：z’-2:(关于~中的更多信息。e) & ?= 1 .（第4节）然后，我们开始了一系列的论文，并将一些关于c.扩展吸引子在古代流形JI中的位置的结果进行验证。这意味着。我们对（m.a）和(H)对有兴趣。l)。1)其中R(。1)表示的IJahill。我即. .所有吸引点的集合I，？-4。本文的目的是介绍一些概念（喧嚣的社区），并促进社区的发展。
1. Introduction. In the dynamics defined hy a diffeomorphism f: M-M of a kniooth (ie C-) m-dimensional manifold 31 attractors (ie com1) act/-invariant suI~ hets, l of ill which attract allpointspnear-1 inthesensethat lini dint (f"(p).-1)==(1 holds) play a central role. The attractors whoae intrinsic structure is understnod hest are the expanding attractors which are characterized hy the fact that there is a real numher A> 1 sueh that the restricbtion of f to A expiids the distance hetween sufficiently close points on. 1 l) y a factor ri,(for precise definitions he (+ Iichw). The topological structure of these attractors ww descrihed I)? R. I=.\lvmdrAm [7].[$ I, f9]. He proved that an n-dimensional expanding attractor 1 IS lo call^ homeomorphic to the cartesian 1) roduct of an n-dimensional ball ttnd a C~.\STOH. set, while the glohal structure of. I and the dynamics of f on. I can lie described by 8 topological space L'which is like an n-manifold with certain t) ranch] mints and an expanding mapping: z'-2:(For some more information in the~. e) &?= 1 hee Section 4.) Heie we start a series of papers in wliicti some results concerning the psition ot c. xpanding attravtors in the anihient manifold JI will I e]) roved. This mean.: that we are interested in the pairs (M. A) and (H (. l),. 1) where R (. 1) denotes the IJahill of. I ie.. the set of all pointh which are attracted I,?-4. The aim of the present (faller is to introduce some concepts (the tuhular neightmrhoods) and to pro\t'