Empirical definition
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The statement of the theorem
From an empirical perspective, all dynamical systems derived from temporal data
are discrete, Gauss for example proved that with the measurement of 3 positions and times of Ceres in the sky is possible to fully determine the orbit, therefore be able to compute any possible position and velocity of the asteroid in the past or the future and therefore fully characterize the dynamical system. Typical tasks with experimental data are to derive a mathematical model.
- ^https://sites.math.rutgers.edu/~cherlin/History/Papers1999/weiss.html
- ^Moore, Samuel A.; Mann, Brian P.; Chen, Boyuan (17 December 2025). "Automated global analysis of experimental dynamics through low-dimensional linear embeddings". npj Complexity. 2 (1) 36. doi:10.1038/s44260-025-00062-y.