Banach spaces adapted to Anosov systems
Banach spaces adapted to Anosov systems
复制标题
适应 Anosov 系统的 Banach 空间
DOI：
10.1017/s0143385705000374
复制
发表时间：
2004
影响因子：
0.9
通讯作者：
C. Liverani
中科院分区：
文献类型：
--
作者：
S. Gouezel;C. Liverani
研究了具有高光滑性的函数类上与Anosov映射相关的Ruelle-Perron-Frobenius算子的谱性质。为此，我们构造了转移算子在其上具有小本质谱的各向异性分布的Banach空间。在${\mathcal C}^\ininfty$的情况下，本质谱半径是任意小的，这给出了具有任意精度的关联的描述。此外，对于确定性扰动和随机扰动，我们得到了精确的谱稳定性结果。特别地，我们得到了谱数据的可微性结果(它包含了Sinai-Ruelle-Bowen测度的可微性、中心极限定理的方差、光滑可观测量的衰减率等)。
We study the spectral properties of the Ruelle–Perron–Frobenius operator associated to an Anosov map on classes of functions with high smoothness. To this end we construct anisotropic Banach spaces of distributions on which the transfer operator has a small essential spectrum. In the ${\mathcal C}^\infty$ case, the essential spectral radius is arbitrarily small, which yields a description of the correlations with arbitrary precision. Moreover, we obtain sharp spectral stability results for deterministic and random perturbations. In particular, we obtain differentiability results for spectral data (which imply differentiability of the Sinai–Ruelle–Bowen measure, the variance for the central limit theorem, the rates of decay for smooth observable, etc.).