Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances
Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances
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Anosov 微分同胚和 Ruelle 共振的半经典方法
DOI：
10.2174/1874117700801010035
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Johannes Sjoestrand
中科院分区：
文献类型：
--
作者：
Frédéric Faure;Nicolas Roy;Johannes Sjoestrand
在这篇文章中，我们证明了Anosov微分同态的一些谱性质可以通过半经典分析得到。特别是，在Aguar-Baslev-Combes理论或最近的Helffer-Sjostrand相空间理论中，Ruelle共振可以被视为开放量子系统的量子共振，Ruelle共振是作用于合适的各向异性Sobolev空间中的Ruelle转移算符的本征值，它控制着动力学关联的衰变。
In this paper, we show that some spectral properties of Anosov diffeomorphisms can be obtained by semi-classical analysis. In particular the Ruelle resonances which are eigenvalues of the Ruelle transfer operator acting in suitable anisotropic Sobolev spaces and which govern the decay of dynamical correlations, can be treated as the quantum resonances of open quantum systems in the Aguilar-Baslev-Combes theory or the more recent Helffer-Sjostrand phase-space theory.