On the consequences of resonant returns of near-earth asteroids

Possible collisions of asteroids with the Earth associated with resonant returns are considered. The list of more than 100 collisions of asteroid Apophis in XXI century derived in the Chair of Celestial Mechanics SPbSU is discussed, including relative positions and sizes of gaps, leads to collisions. In spite of orbit refinement in 2013, Apophis will be a hazardous asteroid. Main characteristics of gaps leading to collisions are stable under small change of the model of motion. Due to resonant returns relative positions of gaps form complicated structure, similar to a fractal structure. This structure must be taken into account for the design of collisions eliminating. The results derived by NASA concerning asteroid Apophis are discussed as well. They are in good agreement with our results. Connected with resonant returns peculiarities of Apophis trajectory holds true for other hazardous asteroids. It is very important to investigate this peculiarities carefully.