Combinatorial approximation by Devaney-chaotic or periodic volume preserving homeomorphisms
Combinatorial approximation by Devaney-chaotic or periodic volume preserving homeomorphisms
复制标题
通过 Devaney 混沌或周期性体积保持同胚的组合逼近
DOI：
10.1142/s0218127499000596
复制
发表时间：
1999
影响因子：
2.2
通讯作者：
S. Alpern
中科院分区：
文献类型：
--
作者：
S. Alpern
本文修改了Peter Lax的一个组合思想，用另一个保体积同胚一致逼近闭单位立方体In（n≥2）的任何保体积同胚，该同胚要么（i）严格置换总体积为1的并矢立方体的无限族，要么（ii）在Devaney意义下是混沌的.我们的方法也适用于任意紧致流形赋予一个非原子，局部正Borel措施。
We modify a combinatorial idea of Peter Lax, to uniformly approximate any volume preserving homeomorphism of the closed unit cube In, n≥2, by another one which either: (i) rigidly permutes an infinite family of dyadic cubes of total volume one, or (ii) is chaotic in the sense of Devaney. Our methods apply as well to arbitrary compact manifolds endowed with a nonatomic, locally positive Borel measure.