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arXiv · 2304.00089

On the Objectivity and Quasi-Objectivity of TSE and TRA

Holger Theisel·Anke Friederici·Tobias Günther
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Abstract

We analyze two recently-introduced flow measured that are based on a single trajectory only: trajectory stretching exponent (TSE) to detect hyperbolic (stretching) behavior, and trajectory angular velocity (TRA) to detect elliptic (rotation) behavior. Haller et al. [2021] and Haller et al. [2022] introduced TSE, TRA as well as the concept of quasi-objectivity, and formulated theorems about the objectivity and quasi-objectivity of TSE and TRA. In this paper, we present two counter-examples showing that all theorems in Haller et al. [2021] and Haller et al. [2022] are incorrect.

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Holger Theisel, Anke Friederici, Tobias Günther. 2023-03-31. On the Objectivity and Quasi-Objectivity of TSE and TRA. https://arxiv.org/abs/2304.00089

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