THE UNIVERSAL TRANSITION OF PLATEAU STRUCTURE OF LYAPUNOV EXPONENTS

The universal transition of Lyapunov exponents between conservative li mit and dissipative limit of nonlinear dynamical system is studied. It is discovered numerically and proved analytically that for homogeneou s dissipative two-dimensional maps, along the equal dissipation line i n parameter space, the Lyapunov exponents of attractor orbits possess a plateau structure and strict symmetry about its plateau value. The r atios between the plateau width and the stable window width of period 1-4 orbits for Henon map are calculated. The result shows that the pla teau structure of Lyapunov exponents remains invariant for the attract or orbits belonging to a period doubling bifurcation sequence. This fa ct reveals a new universal transition behavior between order and chaos when the dissipation of the dynamical system is weakened to zero.