23 citations · 75 across the 13 of their papers we have counts for
13 papers
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…
Convergence of spectra of digraph limits
Jan Grebík, Daniel Král', Xizhi Liu +2
The relation between densities of cycles and the spectrum of a graphon, which implies that the spectra of convergent graphons converge, fundamentally relies on the self-adjointness…
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…
Lagrange approximation of transfer operators associated with holomorphic data
Oscar F. Bandtlow, Julia Slipantschuk
We show that spectral data of transfer operators given by holomorphic data can be approximated using an effective numerical scheme based on Lagrange interpolation. In particular, w…
Transfer operator approach to ray-tracing in circular domains
J Slipantschuk, M Richter, D J Chappell +3
The computation of wave-energy distributions in the mid-to-high frequency regime can be reduced to ray-tracing calculations. Solving the ray-tracing problem in terms of an operator…
Dynamic mode decomposition for analytic maps
Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just
Extended dynamic mode decomposition (EDMD) provides a class of algorithms to identify patterns and effective degrees of freedom in complex dynamical systems. We show that the modes…
Spectral structure of transfer operators for expanding circle maps
Oscar F. Bandtlow, Wolfram Just, Julia Slipantschuk
We explicitly determine the spectrum of transfer operators (acting on spaces of holomorphic functions) associated to analytic expanding circle maps arising from finite Blaschke pro…
Analytic expanding circle maps with explicit spectra
Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just
We show that for any with there exists an analytic expanding circle map such that the eigenvalues of the associated transfer operator (acting on holomorph…
On the relation between Lyapunov exponents and exponential decay of correlations
Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just
Chaotic dynamics with sensitive dependence on initial conditions may result in exponential decay of correlation functions. We show that for one-dimensional interval maps the corres…