Strong orbit realization for minimal homeomorphisms
Strong orbit realization for minimal homeomorphisms
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最小同胚的强轨道实现
DOI：
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发表时间：
1997
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影响因子：
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通讯作者：
N. Ormes
中科院分区：
文献类型：
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作者：
N. Ormes
设X是Cantor集，S是X的极小自同胚，Μ是不变的Borel概率。设为非原子勒贝格概率空间(Y，Ν)的遍历自同构。则有一个极小同胚S‘具有相同的轨道ASS使得(S’，Μ)与(T，Ν)可测共轭。当且仅当周期谱OFS包含在离散谱OFT中时，才能选择强轨道等价于S。这些结果的推论推广了Dye定理和Juett-Krieger定理。
LetXbe a Cantor set,S a minimal self-homeomorphism ofX, and Μ anS-invariant Borel probability. LetT be an ergodic automorphism of a non-atomic Lebesgue probability space(Y,Ν). Then there is a minimal homeomorphismS′ with the same orbits asS such that (S′, Μ ) is measurably conjugate to (T, Ν). HereS′ can be chosen strongly orbit equivalent toS if and only if the periodic spectrum ofS is contained in the discrete spectrum ofT. Corollaries of these results generalize Dye’s Theorem and the Jewett-Krieger Theorem.