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tokens: were a ≈ 1730 au and e ≈ 0.99999, corresponding to separation at pericentre d per ≈ 3.8 R ⊙ and the companion filling its Roche lobe 89 per cent (radius-wise), which is sufficient for circularization in all our models. Fig. 3 shows the detailed evolution of the binary orbital parameters a and e , as well as the pericentre separation d per . Even though the binary was affected by more than 5000 encounters, the vast majority of interactions had very little effect on its orbit, with only a few inducing significant changes of orbital parameters. The average mass of fly-by stars in the only 10 encounters during which the orbital energy was changed by more than 10 per cent was ∼13.5 M ⊙ , whereas the average mass of all stars encountered by the binary was ∼0.62 M ⊙ . In fact, it is very typical for the majority of dynamically formed LMXBs in our simulations that the dynamic evolution of a binary is mainly dependent on a few key encounters with, on average, exceptionally massive fly-bys. This is connected to the fact that, on average, the amplitude of a velocity kick induced by a fly-by to one binary component with respect to the other can be analytically estimated as proportional to the fly-by's mass (e.g. Hills 1981 ), i.e. Here, a is the semimajor axis of the binary, M fly-by is the mass of the fly-by, b is the impact parameter and v rel is the fly-by's velocity, relative to the mass centre of the binary. This suggests that the local stellar mass distribution has influence on the time-scale of evolution through dynamical interactions and therefore the effectiveness of the LMXB's dynamical formation channel. We discuss this further in Section 5.2 . Figure 3. Detailed evolution of orbital parameters a and e , as well as distance at pericentre d per = a (1 − e ) for an exemplary, typical binary that has undergone tidal circularization (noticeable as a rapid decrease of both semimajor axis and eccentricity at the very end of evolution). This particular system was subject to over 5000 stellar encounters, most of them occurring during the second half of its evolution. The binary was subject to several major changes of orbital parameters as a result of encounters with exceptionally massive fly-bys. For instance, the most significant change of eccentricity from 0.71 to 0.09 at around 3.7 Gyr (coupled with an increase of the semimajor axis from 345 to 530 au) was caused by an interaction with a ∼4.5-M ⊙ star, whereas the mean mass of fly-bys in our simulations is ∼0.62 M ⊙ . Additionally, the encountered star was passing by with a relatively low speed of ∼45 km s −1 with respect to the binary (the mean relative speed of all fly-bys is ∼125 km s −1 ), which granted an exceptionally long time of gravitational interaction. 4.2 Evolution of orbital parameters The evolution of orbital parameters in Fig. 3 also illustrates a general trend of steadily increasing semimajor axis. This is an average regularity for all of our evolutionary paths leading towards