Ptolemy's Equant Equates to a Universal Dynamical Clock via Machine Learning
Oscillatory dynamics arise ubiquitously in nonlinear systems, yet identifying a physically interpretable phase and phase dynamics in nonlinear, high-dimensional oscillations remains a central unresolved problem. Here we establish the principle of a universal dynamical clock, a physical perspective in which oscillations of arbitrary dimensionality and geometry are equivalently represented as uniform rotation through an equant-induced nonlinear viewing coordinate, inspired by Ptolemy's equant and formalised through an areal-uniformity principle reminiscent of Kepler's second law. Using a machine-learning framework, we demonstrate the existence of such an equant for a broad class of oscillat...
| Authors | Jingdong Zhang, Luan Yang, Murilo S. Baptista et al. |
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| Primary category | math.DS |
| Published | 16 July 2026 |
| Last updated at source | 16 July 2026 |
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