Reconstruction of a system's dynamics from short trajectories

Long data sets are one of the prime requirements of time series analysis techniques to unravel the dynamics of an underlying system. However, acquiring long data sets is often not possible. In this paper, we address the question of whether it is still possible to understand the complete dynamics of a system if only short (but many) time series are observed. The key idea is to generate a single long time series from these short segments using the concept of recurrences in phase space. This long time series is constructed so as to exhibit a dynamics similar to that of a long time series obtained from the corresponding underlying system.