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 Db = 2-$\beta$. The behaviour of m0(k) and Db(k) is studied numerically.
Received: 25 August 1992
Accepted manuscript online:
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