Stickiness effects in chaos

Stickiness is a temporary confinement of orbits in a particular region of the phase space before they diffuse to a larger region. In a system of 2-degrees of freedom there are two main types of stickiness (a) stickiness around an island of stability, which is surrounded by cantori with small holes, and (b) stickiness close to the unstable asymptotic curves of unstable periodic orbits, that extend to large distances in the chaotic sea. We consider various factors that affect the time scale of stickiness due to cantori. The overall stickiness (stickiness of the second type) is maximum near the unstable asymptotic curves. An important application of stickiness is in the outer spiral arms of strong-barred spiral galaxies. These spiral arms consist mainly of sticky chaotic orbits. Such orbits may escape to large distances, or to infinity, but because of stickiness they support the spiral arms for very long times.