scholarly journals Building CX peanut-shaped disk galaxy profiles

2018 ◽  
Vol 612 ◽  
pp. A114 ◽  
Author(s):  
P. A. Patsis ◽  
M. Harsoula
Keyword(s):  
Phase Space ◽  
Periodic Orbits ◽  
Three Dimensional ◽  
Resonance Region ◽  
Space Structure ◽  
Jacobi Constant ◽  
Dynamical Mechanism ◽  
Standard Case ◽  
New Model ◽  
Stable Periodic

Context. We present and discuss the orbital content of a rather unusual rotating barred galaxy model, in which the three-dimensional (3D) family, bifurcating from x1 at the 2:1 vertical resonance with the known “frown-smile” side-on morphology, is unstable. Aims. Our goal is to study the differences that occur in the phase space structure at the vertical 2:1 resonance region in this case, with respect to the known, well studied, standard case, in which the families with the frown-smile profiles are stable and support an X-shaped morphology. Methods. The potential used in the study originates in a frozen snapshot of an N-body simulation in which a fast bar has evolved. We follow the evolution of the vertical stability of the central family of periodic orbits as a function of the energy (Jacobi constant) and we investigate the phase space content by means of spaces of section. Results. The two bifurcating families at the vertical 2:1 resonance region of the new model change their stability with respect to that of most studied analytic potentials. The structure in the side-on view that is directly supported by the trapping of quasi-periodic orbits around 3D stable periodic orbits has now an infinity symbol (i.e. ∞-type) profile. However, the available sticky orbits can reinforce other types of side-on morphologies as well. Conclusions. In the new model, the dynamical mechanism of trapping quasi-periodic orbits around the 3D stable periodic orbits that build the peanut, supports the ∞-type profile. The same mechanism in the standard case supports the X shape with the frown-smile orbits. Nevertheless, in both cases (i.e. in the new and in the standard model) a combination of 3D quasi-periodic orbits around the stable x1 family with sticky orbits can support a profile reminiscent of the shape of the orbits of the 3D unstable family existing in each model.

scholarly journals Periodic orbits relevant for the formation of inner rings in barred galaxies

1985 ◽  
Vol 106 ◽  
pp. 543-544
Author(s):  
M. Michalodimitrakis ◽  
Ch. Terzides
Keyword(s):  
Periodic Orbits ◽  
Three Dimensional ◽  
Particle Trapping ◽  
Barred Galaxies ◽  
Future Paper ◽  
Stability Of Periodic Orbits ◽  
Wide Range ◽  
The Galaxy ◽  
Stable Periodic ◽  
The Stability

The study of orbits of a test particle in the gravitational field of a model barred galaxy is a first step toward the understanding of the origin of the morphological characterstics observed in real barred galaxies. In this paper we confine our attention to the inner rings. Inner rings are a very common characteristic of barred galaxies. They are narrow, round or slightly elongated along the bar (with typical axial ratios from 0.7 to near 1.0), and of the same size as the bar. A first step to test the old hypothesis that inner rings consist of stars trapped near stable periodic orbits would be a study of particle trapping around periodic orbits encircling the bar. Such a study is contained in the work of several authors (Danby 1965, de Vaucouleurs and Freeman 1972, Michalodimitrakis 1975, Contopoulos and Papayannopoulos 1980, Athanassoula et al. 1983). In the above works the stability of periodic orbits was studied with respect to perturbations which lie on the plane of motion z = 0 (planar stability). To ensure the possibility of formation of rings, a study of stability with respect to perturbations perpendicular to the plane of motion (vertical stability) is necessary. In this paper we investigate the properties of periodic orbits which we believe to be relevant for the inner-ring problem using a sufficiently general model for the galaxy and sets of values for the parameters which cover a wide range of different possible cases. We also study the stability, planar and vertical, with respect to large perturbations in order to estimate the extent of particle trapping. A detailed numerical investigation of three-dimensional periodic orbits will be given in a future paper.

Study of molecular phase space structure through families of periodic orbits

1989 ◽  
Vol 135 (3) ◽  
pp. 347-356 ◽  
Author(s):  
S.C. Farantos ◽  
M. Founargiotakis ◽  
C. Polymilis
Keyword(s):  
Phase Space ◽  
Periodic Orbits ◽  
Space Structure ◽  
Phase Space Structure ◽  
Families Of Periodic Orbits

scholarly journals 1/1 resonant periodic orbits in three dimensional planetary systems

2014 ◽  
Vol 9 (S310) ◽  
pp. 82-83 ◽  
Author(s):  
Kyriaki I. Antoniadou ◽  
George Voyatzis ◽  
Harry Varvoglis
Keyword(s):  
Phase Space ◽  
Linear Stability ◽  
Periodic Orbits ◽  
Orbital Motion ◽  
Three Dimensional ◽  
Planetary Systems ◽  
Planetary Mass ◽  
Construct Maps ◽  
Mutual Inclination ◽  
Planar Family

AbstractWe study the dynamics of a two-planet system, which evolves being in a 1/1 mean motion resonance (co-orbital motion) with non-zero mutual inclination. In particular, we examine the existence of bifurcations of periodic orbits from the planar to the spatial case. We find that such bifurcations exist only for planetary mass ratios $\rho=\frac{m_2}{m_1}<0.0205$. For ρ in the interval 0<ρ<0.0205, we compute the generated families of spatial periodic orbits and their linear stability. These spatial families form bridges, which start and end at the same planar family. Along them the mutual planetary inclination varies. We construct maps of dynamical stability and show the existence of regions of regular orbits in phase space.

scholarly journals Simple Periodic Orbits in Elliptical Galaxies Modelled by Hamiltonians in 1-1-1 Resonance

1999 ◽  
Vol 172 ◽  
pp. 411-412
Author(s):  
J. Palacián ◽  
P. Yanguas ◽  
S. Ferrer
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Harmonic Oscillator ◽  
Periodic Orbits ◽  
Homogeneous Polynomial ◽  
Three Dimensional ◽  
Discrete Symmetry ◽  
Elliptical Galaxies ◽  
Isotropic Harmonic Oscillator

AbstractWe consider elliptical galactic models, whose dynamical system consists of a three-dimensional isotropic harmonic oscillator plus a potential given by a homogeneous polynomial of degree four with an additional discrete symmetry. We identify families of simple periodic orbits by studying the reduced phase space.

KNOTTED PERIODIC SOLUTIONS OF A LINEAR NONAUTONOMOUS SYSTEM AND SOME RELATED THREE-DIMENSIONAL FLOWS

2012 ◽  
Vol 22 (11) ◽  
pp. 1250280
Author(s):  
JIBIN LI ◽  
XIAOHUA ZHAO
Keyword(s):  
Phase Space ◽  
Periodic Solutions ◽  
Periodic Orbits ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Distinct Type ◽  
Frequency Parameter ◽  
Bounded Region ◽  
Nonautonomous Systems ◽  
Dimensional Phase Space

This paper considers a three-dimensional linear nonautonomous systems. It shows that for every integer frequency parameter value, this system has a distinct type of knotted periodic solutions, which lie in a bounded region of R3. Exact explicit parametric representations of the knotted periodic solutions are given. By using these parametric representations, two series of three-dimensional flows are constructed, such that these three-dimensional autonomous systems have knotted periodic orbits in the three-dimensional phase space.

HOPF BIFURCATION FROM LINES OF EQUILIBRIA WITHOUT PARAMETERS IN MEMRISTOR OSCILLATORS

2010 ◽  
Vol 20 (02) ◽  
pp. 437-450 ◽  
Author(s):  
MARCELO MESSIAS ◽  
CRISTIANE NESPOLI ◽  
VANESSA A. BOTTA
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Orbits ◽  
Initial Conditions ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Fixed Set ◽  
Electronic Element ◽  
Stable Periodic ◽  
Parameter Values

The memristor is supposed to be the fourth fundamental electronic element in addition to the well-known resistor, inductor and capacitor. Named as a contraction for memory resistor, its theoretical existence was postulated in 1971 by L. O. Chua, based on symmetrical and logical properties observed in some electronic circuits. On the other hand its physical realization was announced only recently in a paper published on May 2008 issue of Nature by a research team from Hewlett–Packard Company. In this work, we present the bifurcation analysis of two memristor oscillators mathematical models, given by three-dimensional five-parameter piecewise-linear and cubic systems of ordinary differential equations. We show that depending on the parameter values, the systems may present the coexistence of both infinitely many stable periodic orbits and stable equilibrium points. The periodic orbits arise from the change in local stability of equilibrium points on a line of equilibria, for a fixed set of parameter values. This phenomenon is a kind of Hopf bifurcation without parameters. We have numerical evidences that such stable periodic orbits form an invariant surface, which is an attractor of the systems solutions. The results obtained imply that even for a fixed set of parameters the two systems studied may or may not present oscillations, depending on the initial condition considered in the phase space. Moreover, when they exist, the amplitude of the oscillations also depends on the initial conditions.

Sign in / Sign up

Export Citation Format

Share Document