DYNAMIC BEHAVIOR OF THE CRITICAL 2-INFINITY ATTRACTOR AND CHARACTERIZATION OF CHAOTIC ATTRACTORS AT BIFURCATIONS IN A ONE-DIMENSIONAL MAP

Dynamic behavior of the critical 2(infinity) attractor at the accumula tion point of period doubling in the one-dimensional map x(n+1)=x(n) e xp[ A(1-x(n))] is studied by the sum of the local expansion rates S-n( x(1)) of nearby orbits. The variance ([S-n(X)](2)) exhibits self-simil ar structure. Critical bifurcations such as band merging, crisis, and intermittency are studied in terms of sigma(n)(q)-the variance of fluc tuations of the coarse-grained local expansion rates of nearby orbits.