Fractal basins of escape and the formation of spiral arms in a galactic potential with a bar

Ernst, A.; Peters, Thomas

doi:10.1093/mnras/stu1325

Cited by 32 publications

(30 citation statements)

References 85 publications

(94 reference statements)

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“…When the value of the energy is higher than the energy of escape, the equipotential surfaces open and escape channels emerge through which the test particle can escape to infinity. The literature is replete with research studies on the field of leaking Hamiltonian systems (e.g., Barrio et al, 2009;Ernst & Peters, 2014;Kandrup et al, 1999;Lai & Tél, 2011;Navarro & Henrard, 2001;Zotos, 2014aZotos, ,b, 2015b.…”

Section: Introductionmentioning

confidence: 99%

Escape dynamics and fractal basins boundaries in the three-dimensional Earth-Moon system

Zotos

2016

Astrophys Space Sci

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The orbital dynamics of a spacecraft, or a comet, or an asteroid in the Earth-Moon system in a scattering region around the Moon using the three dimensional version of the circular restricted three-body problem is numerically investigated. The test particle can move in bounded orbits around the Moon or escape through the openings around the Lagrange points L 1 and L 2 or even collide with the surface of the Moon. We explore in detail the first four of the five possible Hill's regions configurations depending on the value of the Jacobi constant which is of course related with the total orbital energy. We conduct a thorough numerical analysis on the phase space mixing by classifying initial conditions of orbits in several two-dimensional types of planes and distinguishing between four types of motion: (i) ordered bounded, (ii) trapped chaotic, (iii) escaping and (iv) collisional. In particular, we locate the different basins and we relate them with the corresponding spatial distributions of the escape and collision times. Our outcomes reveal the high complexity of this planetary system. Furthermore, the numerical analysis suggests a strong dependence of the properties of the considered basins with both the total orbital energy and the initial value of the z coordinate, with a remarkable presence of fractal basin boundaries along all the regimes. Our results are compared with earlier ones regarding the planar version of the Earth-Moon system.

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Section: Introductionmentioning

confidence: 99%

Escape dynamics and fractal basins boundaries in the three-dimensional Earth-Moon system

Zotos

2016

Astrophys Space Sci

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“…Simple nonlinear dynamical systems in which trajectories may escape through an artificial leak [1] placed in the phase space play an important role in recent studies. Various fields of physics deal with either the escape dynamics of the particles or the decay rate of other physical quantities such as sound intensity, light rays, or fractal eigenstates [2][3][4][5][6][7][8]. It has been pointed out that the escape dynamics strongly depends on the leak size, position, and orientation [9][10][11][12][13][14][15] as well as on other pre-defined properties of the leak, for instance, the reflection coefficient [16].…”

Section: Introductionmentioning

confidence: 99%

Escape dynamics through a continuously growing leak

Vanyó

2017

Phys. Rev. E

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We formulate a model that describes the escape dynamics in a leaky chaotic system in which the size of the leak depends on the number of the in-falling particles. The basic motivation of this work is the astrophysical process which describes the planetary accretion. In order to study the dynamics generally, the standard map is investigated in two cases when the dynamics is fully hyperbolic and in the presence of KAM islands. In addition to the numerical calculations, an analytic solution to the temporal behavior of the model is also derived. We show that in the early phase of the leak expansion, as long as there are enough particles in the system, the number of survivors deviates from the well-known exponential decay. Furthermore, the analytic solution returns the classical result in the limiting case when the number of particles does not affect the leak size.

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“…It should be emphasized that if a test particle has energy larger than the energy of escape, this does not necessarily mean that it will certainly escape from the system and even if escape does occur, the time required for the escape to occur may be very long compared with the natural crossing time. The literature is replete with works on the field of Hamiltonian systems with escapes (e.g., [4,23,33,38,55,56,58,59]).…”

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confidence: 99%

Elucidating the escape dynamics of the four hill potential

Zotos¹

2017

Nonlinear Dyn

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The escape mechanism of the four hill potential is explored. A thorough numerical investigation takes place in several types of two-dimensional planes and also in a threedimensional subspace of the entire four-dimensional phase space in order to distinguish between bounded (ordered and chaotic) and escaping orbits. The determination of the location of the basins of escape toward the different escape channels and their correlations with the corresponding escape time of the orbits is undoubtedly an issue of paramount importance. It was found that in all examined cases all initial conditions correspond to escaping orbits, while there is no numerical indication of stable bounded motion, apart from some isolated unstable periodic orbits. Furthermore, we monitor how the fractality evolves when the total orbital energy varies. The larger escape periods have been measured for orbits with initial conditions in the fractal basin boundaries, while the lowest escape rates belong to orbits with initial conditions inside the basins of escape. We hope that our numerical analysis will be useful for a further understanding of the escape dynamics of orbits in open Hamiltonian systems with two degrees of freedom.

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Fractal basins of escape and the formation of spiral arms in a galactic potential with a bar

Cited by 32 publications

References 85 publications

Escape dynamics and fractal basins boundaries in the three-dimensional Earth-Moon system

Escape dynamics and fractal basins boundaries in the three-dimensional Earth-Moon system

Escape dynamics through a continuously growing leak

Elucidating the escape dynamics of the four hill potential

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