This paper deals with the analysis of Hamiltonian Hopf as well as saddle-center bifurcations
in 4-DOF systems defined by perturbed isotropic oscillators (1: 1: 1: 1 resonance), in the …

Abstract The Kustaanheimo–Stiefel transformation of the Kepler problem with a time-
dependent perturbation converts it into a perturbed isotropic oscillator of four-and-a-half …

In this note we will consider reduction techniques for Hamiltonian systems that are invariant
under the action of a compact Lie group $ G $ acting by symplectic diffeomorphisms, and the …

In this paper we review the connection between the Kepler problem and the harmonic
oscillator. More specifically we consider how the Kepler system can be obtained through …

In 4D symplectic maps complex instability of periodic orbits is possible, which cannot occur
in the 2D case. We investigate the transition from stable to complex unstable dynamics of a …

We study the reduction and regularization processes of perturbed Keplerian systems from
an astronomical point of view. Our approach connects axially symmetric perturbed 4-DOF …

The aim of this paper is to study the periodic orbits of the generalized van der Waals
Hamiltonian system. The tool for studying such periodic orbits is the averaging theory …

This paper is devoted to studying Hamiltonian oscillators in 1: 1: 1: 1 resonance with
symmetries, which include several models of perturbed Keplerian systems. Normal forms …

It is shown that the generalized Hopf map ℍ× ℍ→ ℍ× ℝ× ℝ quaternion formulation can be
interpreted as an SO (3) orbit map for a symplectic SO (3) action. As a consequence the …

This work deals with the full reduction of the spatial Kepler system for bounded and
unbounded motions. Precisely, we consider the four-dimensional oscillator associated to the …