Invariant manifolds , phase correlations of chaotic orbits and the spiral structure of galaxies
نویسنده
چکیده
In the presence of a strong m = 2 component in a rotating galaxy, the phase space structure near corotation is shaped to a large extent by the invariant manifolds of the short period family of unstable periodic orbits terminating at L1 or L2. The main effect of these manifolds is to create robust phase correlations among a number of chaotic orbits large enough to support a spiral density wave outside corotation. The phenomenon is described theoretically by soliton-like solutions of a Sine-Gordon equation. Numerical examples are given in an N-Body simulation of a barred spiral galaxy. In these examples, we demonstrate how the projection of unstable manifolds in configuration space reproduces essentially the entire observed bar-spiral pattern.
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