On the spectrum of the transfer operators of a one-parameter family with intermittency transition

We study the transfer operators for a family $F_r:[0,1] \to [0,1]$ depending on the parameter $r\in [0,1]$, which interpolates between the tent map and the Farey map. In particular, considering the action of the transfer operator on a suitable Hilbert space, we can define a family of infinite matrices associated to the operators and study their spectrum by numerical methods.Comment: 6 pages, 3 figure

On the leading eigenvalue of transfer operators of the Farey map with real temperature

We study the spectral properties of a family of generalized transfer operators associated to the Farey map. We show that when acting on a suitable space of holomorphic functions, the operators are self-adjoint and the positive dominant eigenvalue can be approximated by means of the matrix expression of the operators.Comment: 9 pages, 3 figure

ON THE CONNECTION BETWEEN THE DISTRIBUTION OF EIGENVALUES IN MULTIPLE CORRESPONDENCE ANALYSIS AND LOG-LINEAR MODELS ∗

• Multiple Correspondence Analysis (MCA) and log-linear modeling are two techniques for multi-way contingency table analysis having different approaches and fields of applications. Log-linear models are interesting when applied to a small number of variables. Multiple Correspondence Analysis is useful in large tables. This efficiency is balanced by the fact that MCA is not able to explicit the relations between more than two variables, as can be done through log-linear modeling. The two approaches are complementary. We present in this paper the distribution of eigenvalues in MCA when the data fit a known log-linear model, then we construct this model by successive applications of MCA. We also propose an empirical procedure, fitting progressively the log-linear model where the fitting criterion is based on eigenvalue diagrams. The procedure is validated on several sets of data used in the literature. Key-Words: • Multiple Correspondence Analysis; eigenvalues; log-linear models; graphical models; normal distribution. AMS Subject Classification