Jordan blocks in a one-dimensional Markov map

A simple one-dimensional chaotic map, whose spectral decomposition of the Frobenius-Perron operator in the space of polynomials has Jordan block structure is given and analyzed. The Jordan block structure implies that some correlation functions have exponential decay modified by coefficients, which are polynomials in t. Such a correlation is given for this system and a numerical simulation, which agrees with the theoretical prediction is presented.