Chaotic dynamics and fractal structures in experiments with cold atoms

Daza, Álvar; Georgeot, Bertrand; Guéry-Odelin, David; Wagemakers, Alexandre; Sanjuán, Miguel A. F.

doi:10.1103/physreva.95.013629

Cited by 44 publications

(25 citation statements)

References 26 publications

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“…However, a bigger N can be reached only with a smaller size of the square cells, which also have a minimum size to contain at least one of the N A states. To solve this issue, we follow the procedure outlined in [25], in which the square cells are randomly picked in the space of states through a Monte Carlo procedure, allowing us to increase the number of cells N as necessary. In our particular problem, we find that the final value for the basin entropy keeps constant for a number of cells larger than 3 × 10 5 , hence, in the three cases, we used N = 3.5 × 10 5 cells.…”

Section: Basin Entropymentioning

confidence: 99%

Equilibrium Points and Basins of Convergence in the Triangular Restricted Four-Body Problem with a Radiating Body

Osorio-Vargas

González

Dubeibe

2020

Int. J. Bifurcation Chaos

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The dynamics of the four-body problem have attracted increasing attention in recent years. In this paper, we extend the basic equilateral four-body problem by introducing the effect of radiation pressure, Poynting-Robertson drag, and solar wind drag. In our setup, three primaries lay at the vertices of an equilateral triangle and move in circular orbits around their common center of mass. Here, one of the primaries is a radiating body and the fourth body (whose mass is negligible) does not affect the motion of the primaries. We show that the existence and the number of equilibrium points of the problem depend on the mass parameters and radiation factor. Consequently, the allowed regions of motion, the regions of the basins of convergence for the equilibrium points, and the basin entropy will also depend on these parameters. The present dynamical model is analyzed for three combinations of mass for the primaries: equal masses, two equal masses, different masses. As the main results, we find that in all cases the libration points are unstable if the radiation factor is larger than 0.01 and hence able to destroy the stability of the libration points in the restricted four-body problem composed by Sun, Jupiter, Trojan asteroid and a test (dust) particle. Also, we conclude that the number of fixed points decreases with the increase of the radiation factor.

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Section: Basin Entropymentioning

confidence: 99%

Equilibrium Points and Basins of Convergence in the Triangular Restricted Four-Body Problem with a Radiating Body

Osorio-Vargas

González

Dubeibe

2020

Int. J. Bifurcation Chaos

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“…In the present paper, following the suggestion presented in Ref. [16] we use = 5, for the size of the boxes and = 1 × 10 5 for the total number of boxes, aiming to get a constant and realistic value for .…”

Section: Basin Entropymentioning

confidence: 99%

Exit basins for the Sitnikov problem with variable mass

2020

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In the present paper, we perform a numerical study of the Sitnikov problem aiming to characterize the orbits of a variable mass particle (e.g., comet, rocket, asteroid or spacecraft) and determine the uncertainty in the prediction of the final state of the test particle. The classification of final states was done through the well-known exit basins, while the determination of the uncertainty was calculated using a new tool named Basin entropy. It is found that for small values of the initial mass of the test particle, the number of initial conditions leading to bounded orbits gets increased, thus reducing the uncertainty in the final states. The same behavior in uncertainty is observed for increasing values of the exponent in Jeans law for the variation of the mass. Our results allow us to conclude that: i) an accelerated fuel consumption in the initial stages of stabilization of a satellite can keep the object in an oscillatory state around the primaries and ii) if the mass of the satellite is less than one hundredth of the mass of each primary, it is possible to predict with a very high certainty the final state of the satellite, regardless of the accuracy in the initial conditions of the system.

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“…Following the procedure outlined in [22], once we know the positions of the libration points, we can determine their linear stability by means of the characteristic equation. To do so, we defined a dense, uniform sequence of 10 5 values of δ in the interval [0, 10] and numerically solved the system (8), thus determining the coordinates (x 0 , y 0 ) of the equilibrium points. The last step was to insert the coordinates of the equilibria into the characteristic equation and determine the nature of the four roots.…”

Section: Parametric Evolution Of the Equilibrium Pointsmentioning

confidence: 99%

Basins of convergence of equilibrium points in the generalized Hénon–Heiles system

Zotos

Riaño-Doncel

Dubeibe

2018

International Journal of Non-Linear Mechanics

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We numerically explore the Newton-Raphson basins of convergence, related to the libration points (which act as attractors of the convergence process), in the generalized Hénon-Heiles system (GHH). The evolution of the position as well as of the linear stability of the equilibrium points is determined, as a function of the value of the perturbation parameter. The attracting regions, on the configuration (x, y) plane, are revealed by using the multivariate version of the classical Newton-Raphson iterative algorithm. We perform a systematic investigation in an attempt to understand how the perturbation parameter affects the geometry as well as of the basin entropy of the attracting domains. The convergence regions are also related with the required number of iterations.

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Chaotic dynamics and fractal structures in experiments with cold atoms

Cited by 44 publications

References 26 publications

Equilibrium Points and Basins of Convergence in the Triangular Restricted Four-Body Problem with a Radiating Body

Equilibrium Points and Basins of Convergence in the Triangular Restricted Four-Body Problem with a Radiating Body

Exit basins for the Sitnikov problem with variable mass

Basins of convergence of equilibrium points in the generalized Hénon–Heiles system

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