Chaos identification through the auto-correlation function indicator (ACFI). Issue Volume 15:Issue S364(2019) (October 2021)

• Record Type: Journal Article
• Authors: Carruba, Valerio; Aljbaae, Safwan; Domingos, Rita C.; Huaman, Mariela; Barletta, William
• Editors: Celletti, Alessandra; Galeş, Cătălin; Beaugé, Cristian; Lemaître, Anne
• Is Part Of: Proceedings of the International Astronomical Union. Volume 15:Issue S364(2019)
• Page Start: 108
• Page End: 112
• Publication Date: 2021-10
• Subjects: Celestial mechanics -- Asteroid Belt -- Chaotic Motions -- Statistical Methods; Astronomy -- Congresses; Astronomy -- Periodicals; 520
• DOI: 10.1017/S1743921321001307
• Languages: English
• ISSNs: 1743-9213

Abstract

Abstract: Close encounters or resonances overlaps can create chaotic motion in small bodies in the Solar System. Approaches that measure the separation rate of trajectories that start infinitesimally near, or changes in the frequency power spectrum of time series, among others, can discover chaotic motion. In this paper, we introduce the ACF index ( ACFI ), which is based on the auto-correlation function of time series. Auto-correlation coefficients measure the correlation of a time-series with a lagged duplicate of itself. By counting the number of auto-correlation coefficients that are larger than 5% after a certain amount of time has passed, we can assess how the time series auto-correlates with each other. This allows for the detection of chaotic time-series characterized by low ACFI values.