2022
DOI: 10.1002/mma.8564
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Analysis of the escape in systems with four exit channels

Abstract: 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 … Show more

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Cited by 3 publications
(8 citation statements)
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“…If a particle has not left the system for an integration time of 100 units of time, we will consider that it remains trapped in it. In this way, we analyze the dependence of the distribution of short times of escape on β and C and, also, we show that the sequential pattern in the distribution of short times of escape that Navarro et al [22] found in the galactic problem can also be found in the 4-body problem when the value of the Jacobi constant is close to its critical value and, then, the architecture of the projections of the stable manifolds to the Lyapunov orbits located at the openings of the potential well on the surface of section arises clearly.…”
Section: Introductionmentioning
confidence: 86%
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“…If a particle has not left the system for an integration time of 100 units of time, we will consider that it remains trapped in it. In this way, we analyze the dependence of the distribution of short times of escape on β and C and, also, we show that the sequential pattern in the distribution of short times of escape that Navarro et al [22] found in the galactic problem can also be found in the 4-body problem when the value of the Jacobi constant is close to its critical value and, then, the architecture of the projections of the stable manifolds to the Lyapunov orbits located at the openings of the potential well on the surface of section arises clearly.…”
Section: Introductionmentioning
confidence: 86%
“…for ν 1, 2, 3, 4, and being x * ν and y * ν the coordinates of the peripheral primaries. These coordinates can be easily expressed as a function of the angle between the central body and two successive peripheral primaries [21,22]. The Jacobi integral of motion C of this system is given by…”
Section: Equations Of Motion and Curves Of Zero Velocitymentioning
confidence: 99%
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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%