Stable ergodicity for smooth compact Lie group extensions of hyperbolic basic sets
Stable ergodicity for smooth compact Lie group extensions of hyperbolic basic sets
复制标题
双曲基本集的光滑紧致李群延拓的稳定遍历性
DOI：
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发表时间：
2005
影响因子：
0.9
通讯作者：
A. Török
中科院分区：
文献类型：
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作者：
M. Field;I. Melbourne;A. Török
我们得到了C2双曲同态的双曲基集上紧连通李群扩张的传递性、遍历性和混合性的泛生性和稳定性的精确结果。与以前的工作相比，我们的结果适用于一般双曲基集，并且对于所有r > 0，在Cr-拓扑中是有效的（这里r不必是整数，C1被Lipschitz取代）。此外，当$rge 2 $，我们表明，有一个C2-开和Cr-稠密的子集的Cr-扩张遍历。我们得到了类似的结果稳定的传递性（非紧）$mathbb{R}^m$-扩展，从而推广的结果Nijuichte和Pollicott，和稳定的混合悬浮液流。
We obtain sharp results for the genericity and stability of transitivity, ergodicity and mixing for compact connected Lie group extensions over a hyperbolic basic set of a C2 diffeomorphism. In contrast to previous work, our results hold for general hyperbolic basic sets and are valid in the Cr-topology for all r > 0 (here r need not be an integer and C1 is replaced by Lipschitz). Moreover, when $rge2$, we show that there is a C2-open and Cr-dense subset of Cr-extensions that are ergodic. We obtain similar results on stable transitivity for (non-compact) $mathbb{R}^m$-extensions, thereby generalizing a result of Niţică and Pollicott, and on stable mixing for suspension flows.