Related papers: Testing a Fast Dynamical Indicator: The MEGNO
In this paper we provide an extensive analysis of the global dynamics of high-area-to-mass ratios geosynchronous (GEO) space debris, applying a recent technique developed by Cincotta et al. (2000), Mean Exponential Growth factor of Nearby…
We apply the MEGNO (Mean Exponential Growth of Nearby Orbits) technique to the dynamics of Jovian irregular satellites. We demonstrate the efficiency of applying the MEGNO indicator to generate a mapping of relevant phase-space regions…
We describe numerical tools for the stability analysis of extrasolar planetary systems. In particular, we consider the relative Poincare variables and symplectic integration of the equations of motion. We apply the tangent map to derive a…
The orbits of two individual planets in two known binary star systems, \gamma Cephei and HD 196885 are numerically integrated using various numerical techniques to assess the chaotic or quasi-periodic nature of the dynamical system…
The requirement that planetary systems be dynamically stable is often used to vet new discoveries or set limits on unconstrained masses or orbital elements. This is typically carried out via computationally expensive N-body simulations. We…
Using the tools of Differential Geometry, we define a new <<fast>> chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e. "quickly") than the usual tools, like Lyapunov Characteristic Numbers…
The Fast Lyapunov Indicators are functions defined on the tangent fiber of the phase-space of a discrete (or continuous) dynamical system, by using a finite number of iterations of the dynamics. In the last decade, they have been largely…
Trans-Neptunian objects (TNOs) are small, icy bodies in the outer solar system. They are observed to have a complex orbital distribution that was shaped by the early dynamical history and migration of the giant planets. Comparisons between…
Depending on the planetary orbit around the host star(s), a planet could orbit either one or both stars in a binary system as S-type or P-type, respectively. We have analysed the dynamics of the S-type planetary system in HD 196885 AB with…
The outer Solar System contains a large number of small bodies (known as trans-Neptunian objects or TNOs) that exhibit diverse types of dynamical behavior. The classification of bodies in this distant region into dynamical classes --…
The aim of this research work is to compare the reliability of several variational indicators of chaos on mappings. The Lyapunov Indicator (LI); the Mean Exponential Growth factor of Nearby Orbits (MEGNO); the Smaller Alignment Index…
The identification of mean motion resonances in exoplanetary systems or in the Solar System might be cumbersome when several planets and large number of smaller bodies are to be considered. Based on the geometrical meaning of the resonance…
The Lyapunov exponents of a dynamical system measure the average rate of exponential stretching along an orbit. Positive exponents are often taken as a defining characteristic of chaotic dynamics. However, the standard…
The Maximum Eccentricity Method (MEM) is a standard tool for the analysis of planetary systems and their stability. The method amounts to estimating the maximal stretch of orbits over sampled domains of initial conditions. The present paper…
The focus of this paper is on inclination-only dependent lunisolar resonances, which shape the dynamics of a MEO (Medium Earth Orbit) object over secular time scales (i.e. several decades). Following the formalism of arXiv:2107.14507, we…
We introduce index systems, a tool for studying isolated invariant sets of dynamical systems that are not necessarily hyperbolic. The mapping of the index systems mimics the expansion and contraction of hyperbolic maps on the tangent space,…
Magnetic fields pervade astrophysical systems and strongly influence their dynamics. Because magnetic diffusion is usually much faster than system evolution, ancient fields cannot explain the present magnetization of planets, stars, and…
We have developed a novel Monte Carlo method for simulating the dynamical evolution of stellar systems in arbitrary geometry. The orbits of stars are followed in a smooth potential represented by a basis-set expansion and perturbed after…
Galaxies are faint enough when one observes just their light distributions, but in studying their full dynamical structure the stars are spread over the six dimensions of phase space rather than just the three spatial dimensions, making…
The high number of planet discoveries made in the last years provides a good sample for statistical analysis, leading to some clues on the distributions of planet parameters, like masses and periods, at least in close proximity to the host…