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EDMD for expanding circle maps and their complex perturbations
- Publication Year :
- 2023
-
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.<br />Comment: 18 pages, 4 figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2308.01467
- Document Type :
- Working Paper