Conjugacy of real diffeomorphisms. A survey.
Conjugacy of real diffeomorphisms. A survey.
复制标题
实微分同胚的共轭。
DOI：
10.1090/s1061-0022-2010-01130-0
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
M. Roginskaya
中科院分区：
文献类型：
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作者：
A. O’Farrell;M. Roginskaya
给定一个群G，G中的共轭问题是给出一个有效的方法来确定G的两个给定元素f，g是否共轭的问题，即是否存在属于G的h，使得fh = hg。本文讨论了R中区间I上的所有超同态在群I上的共轭性问题。有许多经典的工作对这个问题，解决共轭问题的特殊类别的地图。不幸的是，专家们所知道的许多结果和论点在文献中很难找到，或者根本不存在。我们试图修复这些空白，通过给出一个系统的评论，我们也包括新的结果，共轭分类在一般情况下。
Given a group G, the conjugacy problem in G is the problem of giving an effective procedure for determining whether or not two given elements f, g of G are conjugate, i.e. whether there exists h belonging to G with fh = hg. This paper is about the conjugacy problem in the group Diffeo(I) of all diffeomorphisms of an interval I in R. There is much classical work on the subject, solving the conjugacy problem for special classes of maps. Unfortunately, it is also true that many results and arguments known to the experts are difficult to find in the literature, or simply absent. We try to repair these lacunae, by giving a systematic review, and we also include new results about the conjugacy classification in the general case.