arXiv subjects

Euaggelos E. Zotos

Publications and source records attributed to Euaggelos E. Zotos.

At least 109 records · Page 6Linked to original sources

arXiv2013

Using new dynamical indicators to distinguish between order and chaos in a galactic potential producing exact periodic orbits and chaotic components

The theory of the inverse problem is used in order to find a two dimensional galactic potential generating a mono-parametric family of elliptic periodic orbits. The potential is made up of a two-dimensional harmonic oscillator with perturbing terms of third and fourth degree and can be considered to describe local motion in the central parts of a barred galaxy. Our numerical calculations indicate that the potential produces also other families of orbits and there are cases, where distinct chaotic components are also observed. The numerical experiments suggest that there are regular as well as chaotic orbits supporting the barred structure. We use a variety of dynamical indicators, in order to determine the character of motion. Of significant interest, is the S(g) dynamical spectrum, which is used in order to identify the islandic motion of resonant orbits and also proves to be a very useful and fast indicator, in order to distinguish between regular and chaotic motion. Comparison with other methods for detecting chaos is also discussed. The present results are compared with outcomes from earlier work.

nlin.CD↗

arXiv2013

A rational galactic potential with accurate periodic orbits and quasi-integrals of motion

The motion in a simple, time independent rational galactic potential is studied. The potential is a generalization of a two dimensional harmonic oscillator potential and can be considered to describe plane motion in the central parts of a galaxy. There are cases, where the potential displays accurate periodic orbits, together with large chaotic regions. The starting position of these orbits can be found using analytical arguments. Using a quasi-integral of motion, we study the stability of the central periodic orbit and explain the degree of chaos in the inner regions of the galaxy. Our outcomes are compared with results coming from polynomial potentials with accurate periodic orbits and large chaotic regions.

nlin.CD↗

arXiv2012

Are semi-numerical methods an effective tool for locating periodic orbits in 3D potentials?

A semi-numerical method is used in order to locate the position and calculate the period of periodic orbits in a 3D composite bisymmetrical potential, in a number of resonant cases. The potential consists of a 3D harmonic oscillator and a Plummer sphere. The outcomes are compared with results found using the numerical integration of the equations of motion and the agreement is very good. This agreement strongly suggests, that semi-numerical methods can be used in order to obtain fast and reliable results regarding the position and period of the periodic orbits in 3D composite potentials with a harmonic oscillator part and different kinds of perturbations. Comparison with other methods of obtaining 3D periodic orbits is discussed.

nlin.CD↗

arXiv2012

Transition between order and chaos in a composite disk galaxy model with a massive nucleus and a dark matter halo

We investigate the transition from regular to chaotic motion in a composite galaxy model with a disk-halo, a massive dense nucleus and a dark halo component. We obtain relationships connecting the critical value of the mass of the nucleus or the critical value of the angular momentum, with the mass of the dark halo, where the transition from regular motion to chaos occurs. We also present 3D diagrams connecting the mass of nucleus the energy and the percentage of stars that can show chaotic motion. The fraction of the chaotic orbits observed in the phase plane, as a function of the mass of the dark halo is also computed. We use a semi-numerical method, that is a combination of theoretical and numerical procedure. The theoretical results obtained using the version 8.0 of the Mathematica package, while all the numerical calculations were made using a Bulirsch-Stoer FORTRAN routine in double precision. The results can be obtained in semi-numerical or numerical form and give good description for the connection of the physical quantities entering the model and the transition between regular and chaotic motion. We observe that the mass of the dark halo, the mass of the dense nucleus and the L_z component of the angular momentum, are important physical quantities, as they are linked to the regular or chaotic character of orbits in disk galaxies described by the model. Our numerical experiments suggest, that the amount of the dark matter plays an important role in disk galaxies represented by the model, as the mass of the halo affects, not only the regular or chaotic nature of motion but it is also connected with the existence of the different families of regular orbits. Comparison of the present results with earlier work is also presented.

astro-ph.GA↗

arXiv2012

A new dynamical indicator for chaos detection in galactic Hamiltonian systems

A new dynamical parameter, the f-indicator, is introduced and used in order to distinguish between regular and chaotic motion in galactic Hamiltonian systems. Two kinds of galactic potentials are used: (i) a global potential, which describes the whole galaxy and (ii) a local potential, which is made up of perturbed harmonic oscillators and describes motion near an equilibrium point. The new indicator is based on the energies of the separable system along the x, y and z axis. Comparison between the outcomes obtained using the new dynamical parameter and other methods, such as the maximum Lyapunov Characteristic Exponent (L.C.E), or the S(c) dynamical spectrum, shows that the new dynamical indicator gives fast and reliable results concerning the regular or chaotic character of the orbits. The new indicator was tested in several Hamiltonian systems of two (2D) degrees and three (3D) degrees of freedom.

nlin.CD↗

arXiv2012

Investigating the nature of motion in 3D perturbed elliptic oscillators displaying exact periodic orbits

We study the nature of motion in a 3D potential composed of perturbed elliptic oscillators. Our technique is to use the results obtained from the 2D potential in order to find the initial conditions generating regular or chaotic orbits in the 3D potential. Both 2D and 3D potentials display exact periodic orbits together with extended chaotic regions. Numerical experiments suggest, that the degree of chaos increases rapidly, as the energy of the test particle increases. About 97% of the phase plane of the 2D system is covered by chaotic orbits for large energies. The regular or chaotic character of the 2D orbits is checked using the S(c) dynamical spectrum, while for the 3D potential we use the S(c) spectrum, along with the P(f) spectral method. Comparison with other dynamical indicators shows that the S(c) spectrum gives fast and reliable information about the character of motion.

astro-ph.GA↗

arXiv2012

Application of new dynamical spectra of orbits in Hamiltonian systems

In the present article, we investigate the properties of motion in Hamiltonian systems of two and three degrees of freedom, using the distribution of the values of two new dynamical parameters. The distribution functions of the new parameters, define the S(g) and the S(w) dynamical spectra. The first spectrum definition, that is the S(g) spectrum, will be applied in a Hamiltonian system of two degrees of freedom (2D), while the S(w) dynamical spectrum will be deployed in a Hamiltonian system of three degrees of freedom (3D). Both Hamiltonian systems, describe a very interesting dynamical system which displays a large variety of resonant orbits, different chaotic components and also several sticky regions. We test and prove the efficiency and the reliability of these new dynamical spectra, in detecting tiny ordered domains embedded in the chaotic sea, corresponding to complicated resonant orbits of higher multiplicity. The results of our extensive numerical calculations, suggest that both dynamical spectra are fast and reliable discriminants between different types of orbits in Hamiltonian systems, while requiring very short computation time in order to provide solid and conclusive evidence regarding the nature of an orbit. Furthermore, we establish numerical criteria in order to quantify the results obtained from our new dynamical spectra. A comparison to other previously used dynamical indicators, reveals the leading role of the new spectra.

nlin.CD↗

arXiv2012

Trapped and escaping orbits in an axially symmetric galactic-type potential

In the present article, we investigate the behavior of orbits in a time independent axially symmetric galactic type potential. This dynamical model can be considered to describe the motion in the central parts of a galaxy, for values of energies larger than the energy of escape. We use the classical method of the surface of section, in order to visualize and interpret the structure of the phase space of the dynamical system. Moreover, the Lyapunov Characteristic Exponent (LCE), is used in order to make an estimation of the degree of the chaoticity of the orbits in our galactic model. Our numerical calculations suggest that in this galactic type potential, there are two kinds of orbits: (i) escaping orbits and (ii) trapped orbits which do not escape at all. Furthermore, a large number of orbits of the dynamical system, display chaotic motion. Among the chaotic orbits, there are orbits that escape fast and also orbits that remain trapped for vast time intervals. When the value of the test particle's energy exceeds slightly the energy of escape, the amount of the trapped regular orbits increases, as the the value of the angular momentum increases. Therefore, the extent of the chaotic regions observed in the phase plane decreases as the value of the energy increases. Moreover, we calculate the average value of the escape period of the chaotic orbits and we try to correlate it with the value of the energy and also with the maximum value of the z component of the orbits. In addition, we find that the value of the LCE corresponding to each chaotic region, for different values of the energy, increases exponentially as the value of the energy increases. Some theoretical arguments in order to support the numerically obtained outcomes are presented.

astro-ph.GA↗

arXiv2012

Order and chaos in a galactic model with a strong nuclear bar

We use a composite gravitational galactic model consisting of a disk, a halo, a massive nucleus and a strong nuclear bar, in order to study the connections between global and local parameters in a realistic dynamical system. The local model is constructed from a two-dimensional perturbed harmonic oscillator and can be derived by expanding the global model in the vicinity of the central stable Lagrange equilibrium point. The frequencies of oscillations are not arbitrary, but they are connected with all the parameters involved with the global model. Moreover, the value of the local energy is also connected with the value of the global energy. Low and high energy stars in the global model display chaotic motion. Comparison with previous research reveals that the presence of the massive nucleus is responsible for the chaotic motion of the low energy stars. In the local motion, the low energy stars show interesting resonance phenomena, but the chaotic motion, if any, is negligible. On the contrary, the high energy stars do not show bounded motion in the local model. This is an indication of particular activity near the center of galaxies possessing massive nuclei.

astro-ph.GA↗

arXiv2012

Chaos in a disk galaxy model induced by asymmetries in the dark halo

We study the regular or chaotic nature of motion in a disk galaxy with a dense nucleus and an asymmetric dark halo. Two cases, the 2D model and the 3D model, are investigated. In the 2D model, a considerable fraction of the phase plane is covered by chaotic orbits. Two factors seem to be responsible for the chaotic motion: (i) the dense nucleus and (ii) the asymmetries in the dark halo. Our numerical experiments suggest, that there are several chaotic components on the Poincare phase plane. Different chaotic components are induced by the asymmetries in the halo. Each chaotic component seems to have a different value of the Lyapunov Characteristic Exponent, for small values of the asymmetry parameter and a unique LCE for larger values of the asymmetry parameter. A comparison of the present results with outcomes from previous work is also presented.

astro-ph.GA↗

arXiv2012

Order and chaos in a triaxial galaxy model with a dark halo component

We study the regular or chaotic nature of orbits in a 3D potential describing a triaxial galaxy surrounded by a spherical dark halo component. Our numerical calculations show, that the percentage of chaotic orbits decreases exponentially, as the mass of the dark halo increases. A linear increase of the percentage of the chaotic orbits was observed, as the scale length of the dark halo component increases. In order to distinguish between regular and chaotic character of orbits, we use the total angular momentum Ltot, as a new indicator. Comparison of this new dynamical parameter, with other, previously used chaos indicators, shows that the Ltot gives very fast and reliable results in order to detect the character of orbits in galactic potentials.

astro-ph.GA↗

arXiv2012

Dark halos acting as chaos controllers in asymmetric triaxial galaxy models

We study the regular or chaotic character of orbits in a 3D dynamical model, describing a triaxial galaxy surrounded by a spherical dark halo component. Our numerical experiments suggest that the percentage of chaotic orbits decreases exponentially as the mass of the dark halo increases. A linear increase of the percentage of the chaotic orbits was observed as the scale length of the halo component increases. In order to distinguish between regular and chaotic motion, we chose to use the total angular momentum Ltot of the 3D orbits as a new indicator. Comparison with other, previously used, dynamical indicators, such as the Lyapunov Characteristic Exponent or the P(f) spectral method, shows that the Ltot indicator gives very fast and reliable results for characterizing the nature of orbits in galactic dynamical models.

astro-ph.GA↗

arXiv2012

The nature of orbits in a prolate elliptical galaxy model with a bulge and a dense nucleus

We study the transition from regular to chaotic motion in a prolate elliptical galaxy dynamical model with a bulge and a dense nucleus. Our numerical investigation shows that stars with angular momentum Lz less than or equal to a critical value Lzc, moving near the galactic plane, are scattered to higher z, when reaching the central region of the galaxy, thus displaying chaotic motion. An inverse square law relationship was found to exist between the radius of the bulge and the critical value Lzc of the angular momentum. On the other hand, a linear relationship exists between the mass of the nucleus and Lzc. The numerically obtained results are explained using theoretical arguments. Our study shows that there are connections between regular or chaotic motion and the physical parameters of the system, such as the star's angular momentum and mass, the scale length of the nucleus and the radius of the bulge. The results are compared with the outcomes of previous work.

astro-ph.GA↗

arXiv2012

The evolution of chaos in active galaxy models with an oblate or a prolate dark halo component

The evolution of chaotic motion in a galactic dynamical model with a disk, a dense nucleus and a flat biaxial dark halo component is investigated. Two cases are studied: (i) the case where the halo component is oblate and (ii) the case where a prolate halo is present. In both cases, numerical calculations show that the extent of the chaotic regions decreases exponentially as the scale-length of the dark halo increases. On the other hand, a linear relationship exists between the extent of the chaotic regions and the flatness parameter of the halo component. A linear relationship between the critical value of the angular momentum and the flatness parameter is also found. Some theoretical arguments to support the numerical outcomes are presented. An estimation of the degree of chaos is made by computing the Lyapunov Characteristic Exponents. Comparison with earlier work is also made.

astro-ph.GA↗

arXiv2012

Chaotic orbits in a 3D galactic dynamical model with a double nucleus

A 3D-dynamical model is constructed for the study of motion in the central regions of a disk galaxy with a double nucleus. Using the results of the 2D-model, we find the regions of initial conditions in the (x,px,z,py)=EJ, (y=pz=0) phase space producing regular or chaotic orbits. The majority of stars are on chaotic orbits. All chaotic orbits come arbitrary close to one or to both nuclei. Regular orbits are those starting near the stable periodic orbits of the 2D-system with small values of z0. All regular orbits circulate around only one of the two nuclei.

astro-ph.GA↗

arXiv2012

Using the S(c) spectrum to distinguish between order and chaos in a 3D galactic potential

The regular and chaotic character of orbits is investigated in a 3D potential describing motion in the central parts of a barred galaxy. This potential is an extension in the 3D space of a 2D potential based on a family of figure-eight orbits, which was produced using the theory of the inverse problem. Starting from the results obtained from the 2D system, we proceed to locate the regions in the phase space of the 3D potential, producing regular or chaotic orbits. In order to obtain this we use a new dynamical parameter, the S(c) spectrum, which proves to be a useful and fast indicator in order to distinguish regular motion from chaos in 3D potentials. Comparison with other methods for detecting chaos is also discussed.

astro-ph.GA↗

arXiv2012

A new dynamical model for the study of galactic structure

In the present article, we present a new gravitational galactic model, describing motion in elliptical as well as in disk galaxies, by suitably choosing the dynamical parameters. Moreover, a new dynamical parameter, the S(g) spectrum, is introduced and used, in order to detect islandic motion of resonant orbits and the evolution of the sticky regions. We investigate the regular or chaotic character of motion, with emphasis in the different dynamical models and make an extensive study of the sticky regions of the system. We use the classical method of the Poincare (r-pr) phase plane and the new dynamical parameter of the S(g) spectrum. The LCE is used, in order to make an estimation of the degree of chaos in our galactic model. In both cases, the numerical calculations, suggest that our new model, displays a wide variety of families of regular orbits, compared to other galactic models. In addition to the regular motion, this new model displays also chaotic regions. Furthermore, the extent of the chaotic regions increases, as the value of the flatness parameter b of the model increases. Moreover, our simulations indicate, that the degree of chaos in elliptical galaxies, is much smaller than that in dense disk galaxies. In both cases numerical calculations show, that the degree of chaos increases linearly, as the flatness parameter b increases. In addition, a linear relationship between the critical value of angular momentum and the b parameter if found, in both cases (elliptical and disk galaxies). Some theoretical arguments to support the numerical outcomes are presented. Comparison with earlier work is also made.

astro-ph.GA↗

arXiv2012

Are external perturbations responsible for chaotic motion in galaxies?

We study the nature of motion in a logarithmic galactic dynamical model, with an additional external perturbation. Two different cases are investigated. In the first case the external perturbation is fixed, while in the second case it is varying with the time. Numerical experiments suggest, that responsible for the chaotic phenomena is the external perturbation, combined with the dense nucleus. Linear relationships are found to exist, between the critical value of the angular momentum and the dynamical parameters of the galactic system that is, the strength of the external perturbation, the flattening parameter and the radius of the nucleus. Moreover, the extent of the chaotic regions in the phase plane, increases linearly as the strength of the external perturbation and the flattening parameter increases. On the contrary, we observe that the percentage covered by chaotic orbits in the phase plane, decreases linearly, as the scale length of the nucleus increases, becoming less dense. Theoretical arguments are used to support and explain the numerically obtained outcomes. A comparison of the present outcomes with earlier results is also presented.

astro-ph.GA↗