3 citations · 5 across the 8 of their papers we have counts for
7 papers · 1 filter
Avoiding spectral pollution for transfer operators using residuals
April Herwig, Matthew J. Colbrook, Oliver Junge +2
Koopman operator theory enables linear analysis of nonlinear dynamical systems by lifting their evolution to infinite-dimensional function spaces. However, finite-dimensional appro…
Non-periodic not everywhere dense trajectories in triangular billiards
Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just
Building on tools that have been successfully used in the study of rational billiards, such as induced maps and interval exchange transformations, we provide a construction of a on…
Convergence properties of dynamic mode decomposition for analytic interval maps
Elliz Akindji, Julia Slipantschuk, Oscar F. Bandtlow +1
Extended dynamic mode decomposition (EDMD) is a data-driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin…
A numerical study of rigidity of hyperbolic splittings in simple two-dimensional maps
O. F. Bandtlow, W. Just, J. Slipantschuk
Chaotic hyperbolic dynamical systems enjoy a surprising degree of rigidity, a fact which is well known in the mathematics community but perhaps less so in theoretical physics circl…
EDMD for expanding circle maps and their complex perturbations
Oscar F. Bandtlow, Wolfram Just, Julia Slipantschuk
We show that spectral data of the Koopman operator arising from an analytic expanding circle map can be effectively calculated using an EDMD-type algorithm combining a collocat…
Resonances for rational Anosov maps on the torus
Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just
A complete description of resonances for rational toral Anosov diffeomorphisms preserving certain Reinhardt domains is presented. As a consequence it is shown that every homotopy c…