CORRELATION-FUNCTIONS ON THE BORDER LINES OF TRANSIENT CHAOS

Chaotic properties of a repeller strongly influence the transient prop erties of a system close to it, in particular the correlations in the transient regime. In this paper results are presented for repellers of one-dimensional maps having a fixed point whose Lyapunov exponent agr ees with the escape rate from the repeller: It is proven that the corr esponding natural measure of the repeller is a delta function at the o rigin. Eigenfunctions of the Frobenius-Perron operator are computed. T he correlation function is calculated near the situation of permanent chaos and anomalous decay of the correlations is found. Scaling proper ties are given on the route from a weak repeller to a nonrepeller. The analytic results are supported by numerical calculations.