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Bounding extreme events in dynamical systems over an infinite time horizon — arXiv:2609.30821

Source

arXiv (en)

Original

https://arxiv.org/abs/2609.30821

License (as archived)

CC0-1.0

Archived

2026-10-08T02:56:34.662Z

SHA-256 of the archived text

01d76c6b4f7b5c99fc52a50801d8fea0d34f987198aea6b3d69741c6f169d6cc

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https://metraipolis.com/documento/dc_3bfbffe254d7

How to cite

Bounding extreme events in dynamical systems over an infinite time horizon — arXiv:2609.30821 — arXiv (en), https://arxiv.org/abs/2609.30821 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3bfbffe254d7 (Metraipolis archive dc_3bfbffe254d7, sha256 01d76c6b4f7b5c99fc52a50801d8fea0d34f987198aea6b3d69741c6f169d6cc)

@misc{dc3bfbffe254d7,
  title = {Bounding extreme events in dynamical systems over an infinite time horizon — arXiv:2609.30821},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.30821},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3bfbffe254d7; sha256 01d76c6b4f7b5c99fc52a50801d8fea0d34f987198aea6b3d69741c6f169d6cc},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.30821. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This work addresses the computation of extreme values of observables along trajectories of dynamical systems over an \ks{infinite time horizon}. The setting is intrinsically global: trajectories may exhibit large transient excursions, approach their largest values only asymptotically as time tends to infinity, or escape to infinity in finite time. The proposed framework treats these \mk{ scenarios} in a unified way, so that the resulting extreme values reflect both the transient and the asymptotic behavior of the dynamics. The main difficulty is that neither the time interval nor the state space is assumed to be compact. We address this by combining a radial compactification of the state space with a compactified clock variable and discounted occupation measures. This yields a description of trajectory ensembles on compact sets via occupation measures and the associated Liouville's equation. Extreme values are then characterized through a family of reachability problems for level sets of the observable, which can be solved by a bisection procedure. On the theoretical side, we prove a superposition principle for an infinite-horizon Liouville's equation with a time-distributed terminal measure. This result shows that the measure formulation represents ensembles of stopped admissible trajectories, including trajectories \ks{that never stop}, and establishes equivalence between the trajectory-level and measure-level descriptions.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-28 in math.OC).
Categorie arXiv: Optimization and Control (math.OC) ; Dynamical Systems (math.DS).
Pagina del lavoro: https://arxiv.org/abs/2609.30821 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T02:20:09.731Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-28?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).