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Transfer operators for ultradifferentiable expanding maps of the circle
Ergodic Theory and Dynamical Systems ( IF 0.9 ) Pub Date : 2020-06-11 , DOI: 10.1017/etds.2020.36
MALO JÉZÉQUEL

Given a ${\mathcal{C}}^{\infty }$ expanding map $T$ of the circle, we construct a Hilbert space ${\mathcal{H}}$ of smooth functions on which the transfer operator ${\mathcal{L}}$ associated to $T$ acts as a compact operator. This result is made quantitative (in terms of singular values of the operator ${\mathcal{L}}$ acting on ${\mathcal{H}}$) using the language of Denjoy–Carleman classes. Moreover, the nuclear power decomposition of Baladi and Tsujii can be performed on the space ${\mathcal{H}}$, providing a bound on the growth of the dynamical determinant associated to ${\mathcal{L}}$.

中文翻译:

圆的超微扩展映射的转移算子

给定一个${\mathcal{C}}^{\infty }$扩展地图$T$的圆,我们构造一个希尔伯特空间${\mathcal{H}}$传递算子在其上的平滑函数${\mathcal{L}}$关联到$T$充当紧凑运算符。这个结果是量化的(根据算子的奇异值${\mathcal{L}}$作用于${\mathcal{H}}$) 使用 Denjoy–Carleman 类的语言。此外,核电分解巴拉迪和辻井的表演可以在空间上进行${\mathcal{H}}$,提供与相关的动态行列式增长的界限${\mathcal{L}}$.
更新日期:2020-06-11
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