Analysis of regularity/chaoticity of the globular clusters dynamics on the central region of the Milky Way

We analyzed the regularity/chaoticity of the orbits of 45 globular clusters in the central region of the Galaxy with a radius of 3.5 kpc, which are subject to the greatest influence from an elongated rotating bar. Various analysis methods were used, namely, methods for calculating the Highest Lyapunov Exponents, the method of Poincar$\acute{e}$ sections, the frequency method based on the calculation of fundamental frequencies, as well as the visual assessment method. Bimodality was discovered in the histogram of the distribution of positive Lyapunov exponents, calculated in the classical version, without renormalization of the shadow orbit, which makes it possible to implement a probabilistic method of GC classification. To construct the orbits of globular clusters, we used a gravitational potential model with a bar in the form of a triaxial ellipsoid, described in detail in the work of Bajkova et al., Izvestiya Glavnoi astronomicheskoi observatorii v Pulkove, {\bf 228}, 1 (2023). The following bar parameters were adopted: mass $10^{10} M_\odot $, semimajor axis length 5 kpc, bar viewing angle 25$^o$, rotation velocity 40 km s$^{-1}$ kpc$^{-1}$. To form the 6D-phase space required for orbit integration, the most accurate astrometric data to date from the Gaia satellite (EDR3) (Vasiliev, Baumgardt, 2021), as well as new refined average distances to globular clusters (Baumgardt, Vasiliev, 2021) were used. A classification is made of globular clusters with regular and chaotic dynamics. As the analysis showed, globular clusters with small pericentric distances and large eccentricities are most susceptible to the influence of the bar and demonstrate the greatest chaos. It is shown that the results of classifying globular clusters by the nature of their orbital dynamics, obtained using the various methods of analysis considered in the work, correlate well with each other.