New approach to the correlation spectrum near intermittency: a quantum mechanical analogy

Abstract

The correlation spectrum of fully developed one-dimensional mappings are studied near and at a weakly intermittent situation. Using a suitable infinite matrix representation, the eigenvalue equation of the Frobenius-Perron operator is approximately reduced to the radial Schro"dinger equation of the hydrogen atom. Corrections are calculated by quantum mechanical perturbation theory. Analytical expressions for the spectral properties and correlation functions are derived and checked numerically. Compared to our previous works, the accuracy of the present results is significantly higher owing to the controlled and systematic approximation scheme.