Strong Trajectorial Ontological Differentiation: A novel approach to unravel phase-space structures
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910257488330752 |
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| author | García-Cuadrillero, P. Capitán, J. A. Revuelta, F. |
| author_facet | García-Cuadrillero, P. Capitán, J. A. Revuelta, F. |
| contents | The identification of invariant objects and Lagrangian coherent structures is a cornerstone of dynamical systems. As a consequence, several diagnostic indicators have been established over time, such as the fast Lyapunov indicator, the finite-time Lyapunov exponent, and Lagrangian descriptors, among others. In this work, we introduce the Strong Trajectorial Ontological Differentiation (STOD) as a novel tool to identify phase-space structures. Unlike other indicators, STOD does not rely on the study of the tangent flow; instead, it identifies phase-space structures by comparing trajectories through a component-wise cancellation process inspired on the Ontological Differentiation (OD) that was originally developed for lexical networks [P. García-Cuadrillero, F. Revuelta, J. A. Capitán, Phys. Rev. E 113, 014305 (2026)]. By applying a reversed-time version of STOD (FinSTOD) to five paradigmatic autonomous and non-autonomous systems of increasing complexity, we show the excellent performance of this indicator in the identification of phase-space structures, adding a new useful tool to the chaotic toolbox. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_26344 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strong Trajectorial Ontological Differentiation: A novel approach to unravel phase-space structures García-Cuadrillero, P. Capitán, J. A. Revuelta, F. Chaotic Dynamics The identification of invariant objects and Lagrangian coherent structures is a cornerstone of dynamical systems. As a consequence, several diagnostic indicators have been established over time, such as the fast Lyapunov indicator, the finite-time Lyapunov exponent, and Lagrangian descriptors, among others. In this work, we introduce the Strong Trajectorial Ontological Differentiation (STOD) as a novel tool to identify phase-space structures. Unlike other indicators, STOD does not rely on the study of the tangent flow; instead, it identifies phase-space structures by comparing trajectories through a component-wise cancellation process inspired on the Ontological Differentiation (OD) that was originally developed for lexical networks [P. García-Cuadrillero, F. Revuelta, J. A. Capitán, Phys. Rev. E 113, 014305 (2026)]. By applying a reversed-time version of STOD (FinSTOD) to five paradigmatic autonomous and non-autonomous systems of increasing complexity, we show the excellent performance of this indicator in the identification of phase-space structures, adding a new useful tool to the chaotic toolbox. |
| title | Strong Trajectorial Ontological Differentiation: A novel approach to unravel phase-space structures |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2605.26344 |