We apply Reeb’s theorem to prove the existence of periodic orbits in the rotating Hénon– Heiles system. To this end, a sort of detuned normal form is calculated that yields a reduced system with at most four non degenerate ...

The existence and stability of periodic solutions for different types of perturbations associated to the Charged Restricted Circular Three Body Problem (shortly, CHRCTBP) is tackled using reduction and averaging theories ...

The goal of this paper is to investigate the effects that the replacement of the Coulomb potential by a soft-core Coulomb potential produces in the classical dynamics of a perturbed Rydberg hydrogen atom. As example, we ...

We present a procedure for the normalization of perturbed Keplerian problems in n dimensions based on Moser regularization of the Kepler problem and the invariants associated to the reduction process. The approach allows ...

A family of perturbed Hamiltonians H = 1/2 (x^2 + X^2) − 1/2 (y^2 + Y^2)+1/2 (z^2 + Z^2) + 2[ (x^4 + y^4 + z^4) + (x^2 y^2 + x^2 z^2 + y^2 z^2)] in 1: −1:1 resonance depending on two real parameters is considered. We ...

Within the framework of the planar three-body problem we establish the existence of quasi-periodic motions and KAM 4-tori related to the co-orbital motion of two small moons about a large planet where the moons move in ...

At the beginning of paper [1] there is an error that spreads along the rest of the work and the conclusions are not correct in their present form. Precisely, in Section 2, page 783, there is a contradiction related to the ...

The well-known problem of the nonlinear stability of L4 and L5 in the circular spatial restricted three-body problem is revisited. Some new results in the light of the concept of Lie (formal) stability are presented. In ...