Dependence of the escape from an axially symmetric galaxy on the energy

Navarro, Juan F.

doi:10.1038/s41598-021-87670-5

Cited by 9 publications

(4 citation statements)

References 14 publications

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“…The problem of escaping particles from open Hamiltonian systems is one of the most analyzed topics in nonlinear dynamics [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. In this kind of systems, there exists a finite energy of escape, E e , such that if the energy of the particle is smaller than E e , the equipotential surfaces are closed and the escape from the system is impossible.…”

Section: Introductionmentioning

confidence: 99%

Dependence of the probability of escape on the Jacobi constant in the N-body ring problem without central body

Belgharbi

Navarro

2023

Eur. Phys. J. Plus

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In this work, we perform a numerical exploration of the escape in the N-body ring problem in absence of a central body, for $$4\le N\le 9$$ 4 ≤ N ≤ 9 and ten values of the Jacobi constant. We show how the probability of escape per interval of time varies as a function of the Jacobi constant, finding that, for values of the Jacobi constant smaller than a certain limit value, the probability of escape from the system tends to decrease with time. However, if we consider values of the Jacobi constant larger than this limit value, the probability of escape grows with time, for times of escape smaller than 100 units of time.

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Section: Introductionmentioning

confidence: 99%

Dependence of the probability of escape on the Jacobi constant in the N-body ring problem without central body

Belgharbi

Navarro

2023

Eur. Phys. J. Plus

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“…The analysis of the escape of a test particle from a dynamical system is an active field of research to which many scientists are contributing nowadays. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] The mechanism that explains how the escape from a system takes place is well known: The limiting curve of the basins of escape in a proper surface of section is determined by projecting the stable manifolds to the unstable periodic orbits that are located at the openings of the curves of zero velocity of the system on this surface. However, it is necessary to calculate these limiting curves in each specific system in order to unveil the properties of the escape.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the escape in systems with four exit channels

Navarro

Belgharbi

Martínez-Belda

2022

Math Methods in App Sciences

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In this paper, we have performed a numerical investigation of the escape of a particle from two different dynamical systems with the same number of exit channels. We have chosen specific values of the parameters of the systems so that the openings of the potential well in both systems are approximately of the same size. We have found that, in the galactic system, the distribution of the times of escape follows a sequential pattern that has never been detected before. Moreover, we have proved that this pattern is directly related to the geometry of the stable manifolds to the Lyapunov orbits located at the openings of the potential.Finally, we have shown that the different nature of the two systems affects the way the escape occurs, due to the difference in the geometry of the manifolds to the Lyapunov orbits in both systems.

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“…The exit basins, sets of initial conditions that lead to a certain exit, are a common tool in this kind of systems to ascertain which initial condition regions are unpredictable, since a minimum uncertainty in the initial conditions can hinder the exit prediction. The vast majority of works on open Hamiltonian systems have been devoted to conservative twodimensional problems [7,8]. Nonetheless, these systems have also been studied in the presence of external perturbations, such as periodic driving [9], additive noise [10] or weak dissipation [11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Weak dissipation drives and enhances Wada basins in three-dimensional chaotic scattering

Fernández,

Seoane,

Sanjuán

2022

Preprint

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Chaotic scattering in three dimensions has not received as much attention as in two dimensions so far. In this paper, we deal with a three-dimensional open Hamiltonian system whose Wada basin boundaries become non Wada when the critical energy value is surpassed in the absence of dissipation. In particular, we study here the dissipation effects on this topological change, which has no analogy in two dimensions. Hence, we find that non-Wada basins, expected in the absence of dissipation, transform themselves into partially Wada basins when a weak dissipation reduces the system energy below the critical energy. We provide numerical evidence of the emergence of the Wada points on the basin boundaries under weak dissipation. According to the paper findings, Wada basins are typically driven, enhanced and, consequently, structurally stable under weak dissipation in three-dimensional open Hamiltonian systems.

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Dependence of the escape from an axially symmetric galaxy on the energy

Cited by 9 publications

References 14 publications

Dependence of the probability of escape on the Jacobi constant in the N-body ring problem without central body

Dependence of the probability of escape on the Jacobi constant in the N-body ring problem without central body

Analysis of the escape in systems with four exit channels

Weak dissipation drives and enhances Wada basins in three-dimensional chaotic scattering

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