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The merits of a perturbation theory based on a mean to osculating transformation that is pure periodic in the fast angle are investigated. The exact separation of the purely short-period effects of the perturbed Keplerian dynamics from the…
This is a review of the Cold Dark Matter model of structure formation, and its variants. The approach is largely from first principles, the main aim being to impart a basic understanding of the relevant theory with an eye to the likely…
A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local…
We study the bifurcation structure of highly inclined near halo orbits with close approaches to the light primary, in the circular restricted three-body problem (CR3BP). Using a Hamiltonian formulation together with Moser regularization, we…
In the framework of the spatial circular Hill three-body problem we illustrate the application of symplectic invariants to analyze the network structure of symmetric periodic orbit families. The extensive collection of families within this…
Classical chaotic systems with symbolic dynamics but strong pruning present a particular challenge for the application of semiclassical quantization methods. In the present study we show that the technique of periodic orbit quantization by…
We construct models of rotating stars using the perturbative approach introduced by J. Hartle in 1967, and a set of equations of state proposed to model hadronic interactions in the inner core of neutron stars. We integrate the equations of…
The significant orbital eccentricities of most giant extrasolar planets may have their origin in the gravitational dynamics of initially unstable multiple planet systems. In this work, we explore the dynamics of two close planets on…
Studying the albedos of the planets and moons of the Solar System dates back at least a century. Of particular interest is the relationship between the albedo measured at superior conjunction, known as the ``geometric albedo", and the…
A theoretical framework for emission originating from rapidly rotating oblate compact objects is described in detail. By using a Hamilton-Jacobi formalism, we show how the special relativistic rotational effects such as aberration of…
A pure two-body problem has seven integrals including the Kepler energy, the Laplace vector, and the angular momentum vector. However, only five of them are independent. When the five independent integrals are preserved, the two other…
Eccentricity of binary systems is not a gauge invariant quantity, but has an important impact on the observed gravitational wave signal of such systems, generating power in all possible harmonics of the orbital period. We here clarify the…
We present an analytical formalism to study the secular dynamics of a system consisting of N-2 planets orbiting a binary star in outer orbits. We introduce a canonical coordinate system and expand the disturbing function in terms of…
The interaction between a planet located in the inner region of a disc and the warped outer region is studied. We consider the stage of evolution after the planet has cleared-out a gap, so that the planetary orbit evolves only under the…
Vertical thermal convection system exhibits weak turbulence and spatio-temporally chaotic behaviour. In this system, we report seven equilibria and 26 periodic orbits, all new and linearly unstable. These orbits, together with four…
We report on a thorough dielectric investigation of the glass-like freezing of the orbital reorientation-dynamics, recently found for the crystalline sulpho-spinels FeCr2S4 and FeSc2S4. As the orbital reorientations are coupled to a…
The orbit decomposition is given under the automorphism group on the real split Jordan algebra of all hermitian matrices of order three corresponding to any real split composition algebra, or the automorphism group on the complexification,…
Orbit-determination programs find the orbit solution that best fits a set of observations by minimizing the RMS of the residuals of the fit. For near-Earth asteroids, the uncertainty of the orbit solution may be compatible with trajectories…
We investigate the evolution of families of periodic orbits in a bisymmetrical potential made up of a two-dimensional harmonic oscillator with only one quartic perturbing term, in a number of resonant cases. Our main objective is to compute…
We consider the planar circular restricted three-body problem (PCRTBP), as a model for the motion of a spacecraft relative to the Earth-Moon system. We focus on the Lagrange equilibrium points $L_1$ and $L_2$. There are families of Lyapunov…