摘要： 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→∞, 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-β. The behaviour of m₀(k) and D_b(k) is studied numerically.

Abstract: 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.

中图分类号:  (Numerical simulations of chaotic systems)

• 05.45.Pq

05.45.Df (Fractals) 02.50.Ey (Stochastic processes)