Stability of exoplanetary systems retrieved from scalar time series

Abstract

We propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time series are used to build up the high-dimensional phase space trajectory representing the dynamical evolution of planetary motion. The framework of nonlinear time series analysis and Poincar\'e recurrences allows us to transform the obtained univariate signals into complex networks whose topology carries the dynamical properties of the underlying system. The network-based analysis is able to distinguish the regular and chaotic behaviour not only for synthetic inputs but also for noisy and irregularly sampled real world observations. The proposed scheme does not require neither n-body integration nor best fitting planetary model to perform the stability investigation, therefore, the computation time can be reduced drastically compared to those of the standard numerical methods.