Related papers: Symplectic map description of Halley's comet dynam…
While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between…
We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the "Morse oscillator"). We use the geometry of the level sets to construct explicit expressions for the trajectories as a function of…
Hybrid symplectic integrators such as MERCURY are widely used to simulate complex dynamical phenomena in planetary dynamics that could otherwise not be investigated. A hybrid integrator achieves high accuracy during close encounters by…
Symplectic integrators are a foundation to the study of dynamical $N$-body phenomena, at scales ranging from from planetary to cosmological. These integrators preserve the Poincar\'e invariants of Hamiltonian dynamics. The $N$-body…
We study periodic orbits in the spatial rotating Kepler problem from a symplectic-topological perspective. Our first main result provides a complete classification of these orbits via a natural parametrization of the space of Kepler orbits,…
Holographic functional methods are introduced as probes of discrete time-stepped maps that lead to chaotic behavior. The methods provide continuous time interpolation between the time steps, thereby revealing the maps to be…
We aim at analytically modelling the solar wind proton trajectories during their interaction with a partially ionised cometary atmosphere, not in terms of bulk properties of the flow but in terms of single particle dynamics. We first derive…
A simple model for the Milky Way halo is presented. It has a flat rotation curve in the inner regions, but the density falls off sharply beyond an outer edge. This truncated, flat rotation curve (TF) model possesses a rich family of simple…
We determine the asymptotics of the two-point correlation function for quantum systems with half-integer spin which show chaotic behaviour in the classical limit using a method introduced by Bogomolny and Keating [Phys. Rev. Lett. 77 (1996)…
In order to describe the impact of different geometric structures and constraints for the dynamics of a regular controlled Hamiltonian system, in this paper, we first define a kind of controlled magnetic Hamiltonian (CMH) system, and give a…
We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e. integrals of motion. The core idea of the…
We investigate regular and chaotic two-dimensional (2D) and three-dimensional (3D) orbits of stars in models of a galactic potential consisting in a disk, a halo and a bar, to find the origin of boxy components, which are part of the bar or…
We analyze the orbital dynamics of spherical test bodies in ``black hole surrounded by dark matter halo'' spherically symmetric spacetimes. When the test body pulsates periodically (such as a variable star), altering its quadrupole tensor,…
This series of papers is devoted to an open-ended project aimed at the solution of Hilbert's sixth problem (concerning joint axiomatization of physics and probability theory) proposed to be constructed in the framework of an all-embracing…
We present the systemic Console, a new all-in-one, general-purpose software package for the analysis and combined multiparameter fitting of Doppler radial velocity (RV) and transit timing observations. We give an overview of the…
Operating in the framework of `supmech' (a scheme of mechanics which aims at providing a concrete setting for the axiomatization of physics and probability theory as required in Hilbert's sixth problem; integrating noncommutative symplectic…
We investigate the emergence of chaotic dynamics in collective-coordinate reductions of a driven and spatially modulated $\phi^4$ field describing the motion of topological kinks. Focusing on finite-dimensional effective models, we consider…
We performed an image search for "Comet Holmes," using the Yahoo Web search engine, on 2010 April 1. Thousands of images were returned. We astrometrically calibrated---and therefore vetted---the images using the Astrometry.net system. The…
The study of the morphology of 2D projected maps of galaxy clusters is a suitable approach to infer, from real data, the dynamical state of those systems. We recently developed a new method to recover the morphological features in galaxy…
This paper continues to carry out a foundational study of Banyaga topologies of a closed symplectic manifold [3]. Our intension in writing this paper is to provide several symplectic analogues of some results found in the study of…