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math.DS2023
A Koopman-Takens theorem: Linear least squares prediction of nonlinear time series
Péter Koltai, Philipp Kunde
The least squares linear filter, also called the Wiener filter, is a popular tool to predict the next element(s) of time series by linear combination of time-delayed observations.…
math.DS2023
Non-Classifiability of Kolmogorov Diffeomorphisms up to Isomorphism
Marlies Gerber, Philipp Kunde
We consider the problem of classifying Kolmogorov automorphisms (or -automorphisms for brevity) up to isomorphism. Within the collection of measure-preserving transformations, B…
math.DS2023
Anti-classification results for weakly mixing diffeomorphisms
Philipp Kunde
We extend anti-classification results in ergodic theory to the collection of weakly mixing systems by proving that the isomorphism relation as well as the Kakutani equivalence rela…