MEASURE OF CHAOTIC ORBITS FOR STANDARD MAP

In this paper, the measure m₀ of the chaotic orbits in phase space for standard map is studied. As the nonlinearity parameter k→0, the contribution to chaotic measure m₀(k) is mainly from the stochastic layers near separatrices of resonance regions. As k→\infty, the contribution to non-chaotic measure (1 - m₀(k)) is mainly from the accelerator modes. The behaviour of m₀(k) in these regions is studied analytically and numerically. For medial k value, the chaotic orbit forms a fat fractal, its boundary is a typical fractal with dimension D_b = 2-\beta. The behaviour of m₀(k) and D_b(k) is studied numerically.