Related papers: An overview of the escape dynamics in the Henon-He…
A fractal method to detect, locate and quantify chaos in multi-dimensional-conservative-closed systems, based on the creation of artificial exits, is presented. The method is invariant under space-time changes of coordinates and can be used…
We study the flow of gas in a barred-galaxy model, in which a considerable part of the underlying stable periodic orbits have loops where, close to the ends of the bar, several orbital families coexist and chaos dominates. Such conditions…
We study the planar motion of test particles in gravitational fields produced by an external material halo, of the type found in many astrophysical systems, such as elliptical galaxies and globular clusters. Both the Newtonian and the…
We study the dynamics of non-adiabatic transitions in non-Hermitian multi-level parabolic models where the separations of the diabatic energies are quadratic function of time. The model Hamiltonian has been used to describe the…
In this paper, we will study the statistical behaviors of orbits. Firstly, we will show that for a dynamical systems have the shadowing property or almost specification property, the set of nonrecurrent points has full topological entropy.…
A detailed analysis of the classical nonlinear dynamics of a single driven square potential barrier with harmonically oscillating position is performed. The system exhibits dynamical trapping which is associated with the existence of a…
This paper investigates the difference between the circular and elliptical cases in one-on-one pursuit and evasion problems. Using the simultaneous differential equation derived by Barton and Eliezer, we derive a dynamical system based on…
In this study, the classical two-dimensional potential $V_N=\frac{1}{2}\,m\,\omega^2\,r^2 + \frac{1}{N}\,r^N\,\sin(N\,\theta)$, $N \in {\mathbb Z}^+$, is considered. At $N=1,2$, the system is superintegrable and integrable, respectively,…
This study examines the effect of dark matter halos on the orbital and escape dynamics of stars in the central region of barred galaxies. A three-dimensional gravitational model with a central bulge, bar, disc, and dark matter halo (or…
The Henon-Heiles system was originally proposed to describe the dynamical behavior of galaxies, but this system has been widely applied in dynamical systems by exhibit great details in phase space. This work presents the formalism to…
We present a novel technique, which we term bailout embedding, that can be used to target orbits having particular properties out of all orbits in a flow or map. We explicitly construct a bailout embedding for Hamiltonian systems so as to…
We consider the dynamic escape of a small packet of ultracold atoms launched from within an optical dipole trap. Based on a theoretical analysis of the underlying nonlinear dynamics, we predict that fractal behavior can be seen in the…
Motivated by recent experimental works, we investigate a system of vortex dynamics in an atomic Bose-Einstein condensate (BEC), consisting of three vortices, two of which have the same charge. These vortices are modeled as a system of point…
The emission of electromagnetic waves from a system described by the H\'enon-Heiles potential is studied in this work. The main aim being to analyze the behavior of the system when the damping term is included explicitly into the equations…
Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded…
In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability applying the theory of transient…
The route to chaos and phase dynamics in a rotating shallow-water model were rigorously examined using a five-mode Galerkin truncated system with complex variables. This system is valuable for investigating how large/meso-scales destabilize…
We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then…
The main objective of this work is to determine the character of orbits of stars moving in the meridional $(R,z)$ plane of an axially symmetric time-independent disk galaxy model with a central massive nucleus and an additional spherical…
The dynamics of three coupled bosonic wells (trimer) containing $N$ bosons is investigated within a standard (mean-field) semiclassical picture based on the coherent-state method. Various periodic solutions (configured as $\pi$-like,…