For N-body simulations of dense star clusters, the stability of hierarchical triples is useful to integrate stable few-body systems such as binaries and triples. Traditional stability criteria have difficulty predicting stability in the mixed-region, where both stable and unstable systems coexist. In order to get a clue to deal with such a problem, we investigate the stability of hierarchical triples from the perspective of orbital periodicity, hiring Fourier analysis of orbital element evolution. Fourier analysis reveals that long-lived systems exhibit distinct patterns: their spectra show regularly spaced dominant peaks, while the power in irregular peaks and continuous components remains small. This implies that stable systems evolve in a more periodic manner compared to unstable ones. We further quantify this periodicity and establish a strong correlation between the Fourier power distribution and system lifetimes. These results highlight orbital periodicity as a reliable diagnostic for the stability of hierarchical triples.
