Polynomial diffeomorphisms of C2. VIII: Quasi-expansion
Polynomial diffeomorphisms of C2. VIII: Quasi-expansion
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C2 的多项式微分同胚。
DOI：
10.1353/ajm.2002.0008
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
J. Smillie
中科院分区：
文献类型：
--
作者：
Eric Bedford;J. Smillie
我们引入的概念，拟展开的上下文中的C2的多项式同构。像双曲型同态一样，拟扩张映射在鞍点有一致大的乘子。另一方面，与双曲情形不同，拟扩张映射可以在稳定流形和不稳定流形之间相切。我们以多种方式描述了拟膨胀，并发展了它们所具有的一些结构。拟展开是由极大熵的真实的多项式同态的研究所激发的，我们对极大熵同态的研究依赖于本文的结果。
We introduce the notion of quasi-expansion in the context of polynomial diffeomorphisms of C 2 . Like hyperbolic diffeomorphisms, quasi-expanding maps have uniformly large multipliers at saddle points. On the other hand, unlike the hyperbolic case, quasi-expanding maps can have tangencies between stable and unstable manifolds. We characterize quasi-expansion in a number of ways and develop some of the structure they possess. Quasi-expansion was motivated by the study of real polynomial diffeomorphisms of maximal entropy, and our study of maximal entropy diffeomorphisms relies on the results of this paper.