Related papers: Symplectic map description of Halley's comet dynam…
The orbital elements of comet Halley are known to a very high precision, suggesting that the calculation of its future dynamical evolution is straightforward. In this paper we seek to characterize the chaotic nature of the present day orbit…
Using a purely Newtonian model for the Solar System, we investigate the dynamics of comet 1P/Halley considering in particular the Lyapunov and power spectra of its orbit, using the nominal initial conditions of JPL's Horizons system. We…
We apply a generalized Kepler map theory to describe the qualitative chaotic dynamics around cometary nuclei, based on accessible observational data for five comets whose nuclei are well-documented to resemble dumb-bells. The sizes of…
In this work the Melnikov method for perturbed Hamiltonian wave equations is considered in order to determine possible chaotic behaviour in the systems. The backbone of the analysis is the multi-symplectic formulation of the unperturbed PDE…
According to Munoz-Gutierrez et al. (2015) the orbit of comet 1P/Halley is chaotic with a surprisingly small Lyapunov time scale of order its orbital period. In this work we analyse the origin of chaos in Halley's orbit and the growth of…
Understanding the dynamics of multi--dimensional conservative dynamical systems (Hamiltonian flows or symplectic maps) is a fundamental issue of non-linear science. The Generalized ALignment Index (GALI), which was recently introduced and…
We derive, and discuss the properties of, a symplectic map for the dynamics of bodies on nearly parabolic orbits. The orbits are perturbed by a planet on a circular, coplanar orbit interior to the pericenter of the parabolic orbit. The map…
I investigate whether comet 1P/Halley participates in the 1,151-year planetary quasi-period T* identified in a companion paper (Baiget Orts 2026a, arXiv:2604.03049). Using historical perihelion records spanning 2,225 years (30 apparitions,…
The intention of this article is to illustrate the use of methods from symplectic geometry for practical purposes. Our intended audience is scientists interested in orbits of Hamiltonian systems (e.g. the three-body problem). The main…
The symplectic Wisdom-Holman map revolutionized long-term integrations of planetary systems. There is freedom in such methods of how to split the Hamiltonian and which coordinate system to employ, and several options have been proposed in…
Long-term stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the symplectic map representing the…
In this work we propose a new numerical approach to distinguish between regular and chaotic orbits in Hamiltonian systems, based on the simultaneous integration of both the orbit and the deviation vectors using a symplectic scheme, hereby…
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…
The Kerr-MOG black hole has recently attracted significant research attention and has been extensively applied in various fields. To accurately characterize the long-term dynamical evolution of charged particles around Kerr-MOG black hole,…
Symplectic mappings are discrete-time analogs of Hamiltonian systems. They appear in many areas of physics, including, for example, accelerators, plasma, and fluids. Integrable mappings, a subclass of symplectic mappings, are equivalent to…
Numerical integrations of the Solar System reveal a remarkable stability of the orbits of the inner planets over billions of years, in spite of their chaotic variations characterized by a Lyapunov time of only 5 million years and the lack…
Due to the chaotic nature of the Solar System, the question of its dynamic long-term stability can only be answered in a statistical sense, e.g. based on numerical ensemble integrations of nearby orbits. Destabilization, including…
A symplectic integrator algorithm suitable for hierarchical triple systems is formulated and tested. The positions of the stars are followed in hierarchical Jacobi coordinates, whilst the planets are referenced purely to their primary. The…
We investigate dynamically and statistically diffusive motion in a chain of linearly coupled 2-dimensional symplectic McMillan maps and find evidence of subdiffusion in weakly and strongly chaotic regimes when all maps of the chain possess…