相关论文: Relevance of the 1:1 resonance in galactic dynamic…

This paper illustrates the application of Lie transform normal-form theory to the construction of the 1:2 resonant normal form corresponding to a wide class of natural Hamiltonian systems. We show how to compute the bifurcations of the main…

The study of self-gravitating stellar systems has provided important hints to develop tools of analytical mechanics. In the present contribution we review how to exploit detuned resonant normal forms to extract information on several…

We study the dynamics of the space debris in the 1:1 and 2:1 resonances, where geosynchronous and GPS satellites are located. By using Hamiltonian formalism, we consider a model including the geopotential contribution for which we compute…

We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under $Z_2 \times Z_2$ symmetry. The rich…

We study the dynamics of a two-planet system, which evolves being in a $1/1$ mean motion resonance (co-orbital motion) with non-zero mutual inclination. In particular, we examine the existence of bifurcations of periodic orbits from the…

We investigate the dynamics in a galactic potential with two reflection symmetries. The phase-space structure of the real system is approximated with a resonant detuned normal form constructed with the method based on the Lie transform.…

We present a general analysis of the orbit structure of 2D potentials with self-similar elliptical equipotentials by applying the method of Lie transform normalization. We study the most relevant resonances and related bifurcations. We find…

Two-degree-of-freedom Hamiltonian systems with an elliptic equilibrium at the origin are characterised by the frequencies of the linearisation. Considering the frequencies as parameters, the system undergoes a bifurcation when the…

We use perturbation theory and bifurcation theory to analyze the dynamical behavior of resonances, associated to a model describing a particle moving within a ring around a celestial object. The central body is modeled as a homogeneous…

We present a general analysis of the bifurcation sequences of periodic orbits in general position of a family of reversible 1:1 resonant Hamiltonian normal forms invariant under $\Z_2\times\Z_2$ symmetry. The rich structure of these…

We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitude, is expanded in power series of eccentricities and…

Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…

Hamiltonian normal forms allow for the analytical approximation of center manifold trajectories and their invariant manifolds through the separation of the saddle and center subspaces that make up the dynamics at the collinear libration…

We have numerically explored the stable planetary geometry for the multiple systems involved in a 2:1 mean motion resonance, and herein we mainly study the HD 82943 system by employing two sets of the orbital parameters (Mayor et al. 2004;…

We study the dynamics of the space debris in regions corresponding to minor resonances; precisely, we consider the resonances 3:1, 3:2, 4:1, 4:3, 5:1, 5:2, 5:3, 5:4, where a j:l resonance (with j, l integers) means that the periods of…

This paper deals with the dynamics of time-reversible Hamiltonian vector fields with 2 and 3 degrees of freedom around an elliptic equilibrium point in presence of symplectic involutions. The main results discuss the existence of…

We describe a comprehensive model for systems locked in the Laplace resonance. The framework is based on the simplest possible dynamical structure provided by the Keplerian problem perturbed by the resonant coupling truncated at second…

We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To…

We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic…

The phase-space structure of two families of galactic potentials is approximated with a resonant detuned normal form. The normal form series is obtained by a Lie transform of the series expansion around the minimum of the original…