Galactic haloA galactic halo is an extended, roughly spherical component of a galaxy which extends beyond the main, visible component. Several distinct components of galaxies comprise the halo: the stellar halo the galactic corona (hot gas, i.e. a plasma) the dark matter halo The distinction between the halo and the main body of the galaxy is clearest in spiral galaxies, where the spherical shape of the halo contrasts with the flat disc. In an elliptical galaxy, there is no sharp transition between the other components of the galaxy and the halo.
Bifurcation theoryBifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior.
Hopf bifurcationIn the mathematical theory of bifurcations, a Hopf bifurcation is a critical point where, as a parameter changes, a system's stability switches and a periodic solution arises. More accurately, it is a local bifurcation in which a fixed point of a dynamical system loses stability, as a pair of complex conjugate eigenvalues—of the linearization around the fixed point—crosses the complex plane imaginary axis as a parameter crosses a threshold value.
StarA star is an astronomical object comprising a luminous spheroid of plasma held together by self-gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night; their immense distances from Earth make them appear as fixed points of light. The most prominent stars have been categorised into constellations and asterisms, and many of the brightest stars have proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations.
Oort constantsThe Oort constants (discovered by Jan Oort) and are empirically derived parameters that characterize the local rotational properties of our galaxy, the Milky Way, in the following manner: where and are the rotational velocity and distance to the Galactic Center, respectively, measured at the position of the Sun, and and are the velocities and distances at other positions in our part of the galaxy. As derived below, and depend only on the motions and positions of stars in the solar neighborhood.
