On the convergence of nonstationary solutions of the Perron-Frobenius equation to the invariant density

The generating function for the eigenfunctions of the Frobenius-Perron operator of the chaotic maps that are conjugated (related by invertible differentiable transformations) to the tent (pyramidal) map is found. The nonstationary solutions of the Perron-Frobenius equation are expressed in terms of the eigenfunctions of the Perron-Frobenius operator. In this context the convergence of nonstationary densities to invariant one is analysed. The elements of 0-space of evolution operator are found.