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arXiv · 1906.04144

Transfer operator for ultradifferentiable expanding maps of the circle

Malo Jézéquel
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Abstract

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 $\mathcal{L}$.

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Malo Jézéquel. 2019-06-10. Transfer operator for ultradifferentiable expanding maps of the circle. https://doi.org/10.1017/etds.2020.36

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