Secular dynamics of a number of planetary systems from the TESS catalog

A study was made of the stability of the orbital dynamics of a number of planets discovered based on data analysis from the TESS orbital observatory. For twelve circumstellar planetary systems, characteristic estimates of the Lyapunov time (the time of the predictable dynamics) are obtained and, based on them, conclusions about the character of stability are drawn. The secular orbital dynamics of the ten considered planetary systems is stable. For planet TOI-905 the calculated Lyapunov time is small (less than 3000 years), which indicates a possible inaccuracy in determining the parameters of this planetary system. A detailed analysis of the stability of the secular dynamics of two circumbinary planets - TOI-1338 and TIC 172900988, was carried out. For these planetary systems, stability diagrams are constructed and analyzed, and estimates of the Lyapunov times are obtained. On the stability diagrams of the planet TOI-1338 and TIC 172900988 are located in regions of stable dynamics with large Lyapunov times (more than 7000) years, which confirms the reliability of the parameters of these planetary systems established from the analysis of observations.