## 1 Introduction  
The Moon and its vicinity are of great interest for both science and space exploration. In recent years, the world's major space agencies have been jointly involved in the research and development of a habitable lunar orbital station named the Lunar Orbital Platform-Gateway (LOP-G) [1]. The station is planned to be used as a communication hub, a science laboratory, a short-term habitation module, and a holding area for rovers and other robotic vehicles. The design of fuel-efficient transfers between a low-Earth parking orbit and the near-lunar space is one of the cornerstones for the rapid development of lunar infrastructure. The first steps in the research of lunar transfer's feasibility and characteristics have been made by the Soviet scientist [PERSON] in the early 1950s. His Ph.D. thesis contains the fundamental results about direct flights to the Moon: [PERSON] was the first who answered the questions on the minimum initial speed for a spacecraft to reach the Moon, the existence and basic properties of free-return trajectories, and the sensitivity of a lunar transfer trajectory to initial conditions [2]. [PERSON]'s results played a crucial role in the first lunar missions. Sample trajectories to the Moon, distinguished by a short time of flight (several days) and hyperbolic arrival velocities, were designed by the patched conic approximation method; they require a significant cost to insert a spacecraft into a desired orbit around the Moon and are thus called high-energy trajectories. When we replace the patched conic approximation with the circular restricted three-body problem (CR3 BP), more efficient transfer trajectories--low-energy trajectories--emerge. The smart use of gravity of the primary and secondary celestial bodies enables considerable fuel savings compared to conventional high-energy transfer trajectories with translunarinjection (TLI) and lunar orbit insertion (LOI) impulsive maneuvers. The price for such efficiency is an appreciably increased time of flight: a low-energy transfer takes months instead of days. The first example of a low-energy Earth-Moon transfer trajectory was given by [PERSON] in 1968 [3]. He rigorously proved the existence of such trajectories and revealed their important feature of _ballistic capture_ when no insertion maneuver is required for a spacecraft to be captured by the Moon's gravity. The Keplerian energy (with respect to the Moon) is no longer the first integral in the CR3 BP and naturally changes its sign from positive to negative as the spacecraft approaches the near-Moon region. One may distinguish _interior_ and _exterior ballistic capture_, depending on from which libration point neck, \(L_{1}\) or \(L_{2}\), the spacecraft dives into the Moon's Hill sphere. The former effect has been successfully leveraged in 2003 in the celebrated SMART-1 low-thrust mission [4]. The latter effect was demonstrated even earlier, in 1990, when [PERSON] and [PERSON] designed a rescue trajectory with exterior capture for the Japanese Hiten mission [5] (the very term of ballistic capture seems to be coined by [PERSON] in the late 1980s). In the following paper [6], the same authors investigated the role of the Sun's gravity perturbation more deeply, raising the perigee of a transfer trajectory. [PERSON] compared such a perturbing effect with the second impulse in a classic three-impulse bielliptic transfer. He deduced some analytical estimates useful for a better understanding of the mechanism of capture in the Earth-Moon-Sun system [7]. Following [PERSON]'s ideas, a number of researchers have developed numerical methods of low-energy trajectory design based on the dynamical systems theory.