Dresden 2026 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 8: Nonlinear Dynamics, Synchronization, and Chaos

DY 8.9: Vortrag

Montag, 9. März 2026, 12:00–12:15, ZEU/0118

Transient nature of recurrence based local dimension estimates from finite time series — •Reik V. Donner — Magdeburg-Stendal University of Applied Sciences, Magdeburg, Germany — Potsdam Institute for Climate Impact Research, Potsdam, Germany

Local fractal dimensions are a widely used concept in dynamical system theory. However, comparing their empirical spatial patterns across published works reveals surprising inconsistency with theoretical expectations. This points to the fact that corresponding estimates obtained from finite time series are notoriously spurious. As an example, a very long trajectory of the Lorenz-63 system in its chaotic regime is subsampled in two different ways: generating ensembles of individual state vectors drawn independently at random from the complete record versus ensembles of contiguous time series segments. In the latter situation, which is commonly present in time series analysis, one obtains a broad distribution and non-random spatial pattern of local dimension estimates, while consideration of independent samples provides much more narrowly distributed and spatially unstructured estimates. While finite-time estimates may still be useful for identifying transient structures caused by the proximity to unstable periodic orbits or similar dynamically invariant objects, their practical interpretation for real-world time series should be carefully reconciled.

Keywords: Nonlinear time series analysis; Chaotic dynamics; Fractal dimensions; Recurrence