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arXiv · 2308.01467

EDMD for expanding circle maps and their complex perturbations

Oscar F. Bandtlow·Wolfram Just·Julia Slipantschuk
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Abstract

We show that spectral data of the Koopman operator arising from an analytic expanding circle map $\tau$ can be effectively calculated using an EDMD-type algorithm combining a collocation method of order m with a Galerkin method of order n. The main result is that if $m \geq \delta n$, where $\delta$ is an explicitly given positive number quantifying by how much $\tau$ expands concentric annuli containing the unit circle, then the method converges and approximates the spectrum of the Koopman operator, taken to be acting on a space of analytic hyperfunctions, exponentially fast in n. Additionally, these results extend to more general expansive maps on suitable annuli containing the unit circle.

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Oscar F. Bandtlow, Wolfram Just, Julia Slipantschuk. 2023-08-02. EDMD for expanding circle maps and their complex perturbations. https://arxiv.org/abs/2308.01467

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