Stability of axial orbits in galactic potentials

Belmonte, Cinzia; Boccaletti, Dino; Pucacco, Giuseppe

doi:10.1007/978-1-4020-5325-2_6

Cited by 3 publications

(3 citation statements)

References 23 publications

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“…In Belmonte et al (2006) we have started to investigate the stability of axial orbits in the logarithmic potential, using a normal form truncated to the first order incorporating the resonance: we got quite a satisfactory agreement with other analytical and numerical predictions but, among other things, we pointed out the troubles due to sensible differences between results coming either from the normal form itself ('final' normalizing variables) or from the approximate integral ('initial' physical variables).…”

Section: Discussionmentioning

confidence: 54%

Quantitative predictions with detuned normal forms

Pucacco

Boccaletti

Belmonte

2008

Celest Mech Dyn Astr

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The phase-space structure of two families of galactic potentials is approximated with a resonant detuned normal form. The normal form series is obtained by a Lie transform of the series expansion around the minimum of the original Hamiltonian. Attention is focused on the quantitative predictive ability of the normal form. We find analytical expressions for bifurcations of periodic orbits and compare them with other analytical approaches and with numerical results. The predictions are quite reliable even outside the convergence radius of the perturbation and we analyze this result using resummation techniques of asymptotic series.Comment: Accepted for publication on Celestial Mechanics and Dynamical Astronom

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Section: Discussionmentioning

confidence: 54%

Quantitative predictions with detuned normal forms

Pucacco

Boccaletti

Belmonte

2008

Celest Mech Dyn Astr

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“…which can be considered as 'realistic' for elliptical galaxies, the thresholds (144) give estimates correct within a 10% if compared with numerical computations [Belmonte et al, 2006[Belmonte et al, , 2007. When the first of them is satisfied, loop orbits bifurcate from the 'short-axis' (the y-axial normal mode in the oblate case, the x-axial normal mode in the prolate case [Marchesiello & Pucacco, 2011]).…”

Section: Bifurcation Of Loop Orbits In Natural Systems With Ellipticamentioning

confidence: 87%

Bifurcation Sequences in the Symmetric 1:1 Hamiltonian Resonance

Marchesiello

Pucacco

2016

Int. J. Bifurcation Chaos

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We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under Z 2 × Z 2 symmetry. The rich structure of these classical systems is investigated with geometric methods and the relation with the singularity theory approach is also highlighted. The geometric approach is the most straightforward way to obtain a general picture of the phasespace dynamics of the family as is defined by a complete subset in the space of control parameters complying with the symmetry constraint. It is shown how to find an energy-momentum map describing the phase space structure of each member of the family, a catastrophe map that captures its global features and formal expressions for action-angle variables. Several examples, mainly taken from astrodynamics, are used as applications.

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“…At this point we should emphasize that a Seyfert galaxy is composed of a disk, bulge a central nucleus and a bar. However, our dynamical system has two degrees of freedom and for this type of Hamiltonians we usually adopt single component potentials to model the properties of barred galaxies (e.g., [12,18,19,29,30,36]) or galaxies in general (e.g., [9,20,21,34,63,64,73,106]). This approach allow us to directly determine the effects of the single component potential to the the different types (resonances) of orbits, the amount of chaos, the escape properties and other dynamical aspects.…”

Section: Discussionmentioning

confidence: 99%

Escape dynamics and fractal basin boundaries in Seyfert galaxies

Zotos

2015

Nonlinear Dyn

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The escape dynamics in a simple analytical gravitational model which describes the motion of stars in a Seyfert galaxy is investigated in detail. We conduct a thorough numerical analysis distinguishing between regular and chaotic orbits as well as between trapped and escaping orbits, considering only unbounded motion for several energy levels. In order to distinguish safely and with certainty between ordered and chaotic motion, we apply the Smaller ALingment Index (SALI) method. It is of particular interest to locate the escape basins through the openings around the collinear Lagrangian points L 1 and L 2 and relate them with the corresponding spatial distribution of the escape times of the orbits. Our exploration takes place both in the physical (x, y) and in the phase (x,ẋ) space in order to elucidate the escape process as well as the overall orbital properties of the galactic system. Our numerical analysis reveals the strong dependence of the properties of the considered escape basins with the total orbital energy, with a remarkable presence of fractal basin boundaries along all the escape regimes. It was also observed, that for energy levels close to the critical escape energy the escape rates of orbits are large, while for much higher values of energy most of the orbits have low escape periods or they escape immediately to infinity. We also present evidence obtained through numerical simulations that our model can describe the formation and the evolution of the observed spiral structure in Seyfert galaxies. We hope our outcomes to be useful for a further understanding of the escape mechanism in galaxies with active nuclei.

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Stability of axial orbits in galactic potentials

Cited by 3 publications

References 23 publications

Quantitative predictions with detuned normal forms

Quantitative predictions with detuned normal forms

Bifurcation Sequences in the Symmetric 1:1 Hamiltonian Resonance

Escape dynamics and fractal basin boundaries in Seyfert galaxies

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