EIGENVALUE SPECTRUM OF THE FROBENIUS-PERRON OPERATOR NEAR INTERMITTENCY

The spectral properties of the Frobenius-Perron operator of one-dimens ional maps are studied when approaching a weakly intermittent situatio n. Numerical investigation of a particular family of maps shows that t he spectrum becomes extremely dense and the eigenfunctions become conc entrated in the vicinity of the intermittent fixed point. Analytical c onsiderations generalize the results to a broader class of maps near a nd at weak intermittency and show that one branch of the map is domina nt in the determination of the spectrum. Explicit approximate expressi ons are derived for both the eigenvalues and the eigenfunctions and ar e compared with the numerical results.