Estimation of the quantity of perturbed subharmonics in the problem of plain motion of a celestial body on an elliptic orbit (Q2850454)

The author considers a planar system which describes motion of a celestial body about its mass center on an elliptic orbit around the attracting center under the condition that the orbit eccentricity \( \varepsilon \) is sufficient small. The problem of the quantity of existing periodic solutions of the system as parameter \( \varepsilon \) tends to zero is studied. The main result is the following: the number of subharmonics in the perturbed system is estimated from below by a function which is proportional to square of logarithm of orbit eccentricity \( \varepsilon \to 0\).