1 results
Transfer operators for ultradifferentiable expanding maps of the circle
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 41 / Issue 7 / July 2021
- Published online by Cambridge University Press:
- 11 June 2020, pp. 2049-2068
- Print publication:
- July 2021
-
- Article
- Export citation
-
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 
${\mathcal{L}}$.
