Chaotic properties of a repeller strongly influence the transient properties 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 agrees with the escape rate from the repeller: It is proven that the corresponding natural measure of the repeller is a δ function at the origin. Eigenfunctions of the Frobenius-Perron operator are computed. The correlation function is calculated near the situation of permanent chaos and anomalous decay of the correlations is found. Scaling properties are given on the route from a weak repeller to a nonrepeller. The analytic results are supported by numerical calculations.
|Number of pages||8|
|Journal||Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics|
|Publication status||Published - Jan 1 1996|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics