Analysis of luminosity measurements of the pre-white dwarf PG 1159-035: an approach featuring a dynamical database

In a previous work, those of the luminosity measurements of the pre-white dwarf PG 1159-035 which are available online yielded estimates for the optimal embedding dimension, for the dimensionality of the phase space reconstructed from these observations, and for the maximal Lyapunov exponent $\lambda$: the result $\lambda = (9.2 \pm 1.0 ({\rm stat.}) \pm 2.7 ({\rm syst.})) \cdot 10^{-2}~\Delta \tau^{-1}$($\Delta \tau=10$ s is the sampling interval in the measurements) was obtained, suggesting that the physical processes, underlying the variation of the luminosity of PG 1159-035, are chaotic. An improved approach is employed in the present work in relation to the database of embedding vectors: instead of assigning each of the input time-series arrays either to the training or to the test set, the new approach features the creation of a dynamical database, i.e., of one which depends on the choice of the input test file. Although the size of the database is thus increased by a factor of about $2$ (compared to the previous study), the impact of this change on the important results is found to be insignificant. The estimate of this work for the maximal Lyapunov exponent ($\lambda = (8.9 \pm 0.7 ({\rm stat.}) \pm 1.9 ({\rm syst.})) \cdot 10^{-2}~\Delta \tau^{-1}$) is in very good agreement with the result of the earlier study.