Chaos identification through the autocorrelation function indicator (ACFI)

Abstract

Chaotic motion affecting small bodies in the Solar system can be caused by close encounters or collisions or by resonance overlapping. Chaotic motion can be detected using approaches that measure the separation rate of trajectories that starts infinitesimally close or changes in the frequency power spectrum of time series, among others. In this work, we introduce an approach based on the autocorrelation function of time series, the ACF index (ACFI). Autocorrelation coefficients measure the correlation of a time series with a lagged copy of itself. By measuring the fraction of autocorrelation coefficients obtained after a given time lag that are higher than the 5% null hypothesis threshold, we can determine how the time series autocorrelates with itself. This allows identifying unpredictable time series, characterized by low values of ACFI. Applications of ACFI to orbital regions affected by both types of chaos show that this method can correctly identify chaotic motion caused by resonance overlapping, but it is mostly blind to close encounters induced chaos. ACFI could be used in these regions to select the effects of resonance overlapping.