Multifractal signatures of Hamiltonian chaos in Hyperion's rotational dynamics

The chaotic rotation of Saturn's moon Hyperion constitutes a canonical example of Hamiltonian chaos in a natural physical system. While its tumbling motion is well established theoretically, extracting a robust signature of chaos from sparse and noisy astronomical time series remains a fundamental challenge, rendering phase-space reconstruction methods largely impractical under realistic observational constraints. In this work, we demonstrate that multifractal detrended fluctuation analysis provides an observationally viable alternative for identifying chaotic dynamics directly from photometric time series. By analyzing historical ground-based light curves alongside synthetic data generated from the full three-dimensional Euler-Liouville equations, we show that the multifractality associated with the intermittency inherent to chaotic tumbling is consistent with a broad singularity spectrum. While multifractality is an established feature of Hamiltonian chaos, we show that it provides a novel and observationally viable diagnostic under sparse sampling-where traditional chaos indicators fail. In particular, we show that the multifractal spectrum survives realistic observational filtering and reliably discriminates intrinsic chaotic tumbling from aliased regular rotation in sparse astronomical time series. Conversely, regular resonant rotation exhibits a marked reduction in spectral width, approaching the monofractal limit characteristic of uncorrelated noise. For the observational data, we measure a broad spectral width that is consistent with the synthetic chaotic model, statistically distinct from surrogate datasets, and robust against the finite length of the observational time series. These results demonstrate the viability of multifractal scaling as a positive signature of Hamiltonian chaos in sparse datasets, bridging the gap between nonlinear dynamics theory and planetary photometry.