STICKINESS IN CHAOS

• DOI: 10.1142/s0218127408022172
• Publication Date: 2009-01-19T05:46:54Z
• Authors: G. CONTOPOULOS; M. HARSOULA
• Keywords: Astrophysics (astro-ph); 0103 physical sciences; FOS: Physical sciences; Astrophysics; 01 natural sciences

We distinguish two types of stickiness in systems degrees freedom: (a) around an island stability, and (b) chaos, along the unstable asymptotic curves periodic orbits. In fact, there are orbits near outer boundary that remain close to for some time, then extend large distances into surrounding chaotic sea. But later return contribute overall produces dark regions islands lines extending far from islands. have studied these effects standard map with a rather nonlinearity K = 5, we emphasized role U , S central orbit O (x 0.5, y 0), surround 1 ′ + - simplest . This is 4/9 has 9 points more symmetric The produce positive time direction ( ) negative ). closer make many oscillations before reaching further away escape faster. Nevertheless all times this island. very similar also similar. However, forward direction, different opposite calculated finite LCN (Lyapunov characteristic number) χ( t ), which initially smaller than after long values zone approach same final value lim → ∞ χ(t). stretching number (LCN one iteration only) varies curve going through minima at turning curve. (initial times) initial outside but separate fast slow follow shape explained phenomenon by noting on its inner side (closer point 4/9, say P while their All original arcs isodensity maxima density For pronounced. much longer (about 1000 iterations) reduced distribution sea tends be uniform. 4/9. related fact connected heteroclinic main reason similarity cannot intersect each other.