Spectra of Perron-Frobenius operator and new construction of two dimensional low discrepancy sequences

Compact weighted Frobenius-Perron operators and their spectra

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.

Weighted Frobenius-Perron and Koopman operators

Mixing property and pseudo random sequences

We will give a summary about the relations between the spectra of the Perron–Frobenius operator and pseudo random sequences for 1-dimensional cases. There are many difficulties to construct general theory of higher-dimensional cases. We will give several examples for these cases.

PERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES

We give further results for Perron-Frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. We indicate two techniques for establishing the main theorem ofPerron and Frobenius on the numerical range. In the rst method, we use acorresponding version of Wielandt's lemma. The second technique involves graphtheory.

What is the Use of Frobenius - Perron Operator for Chaotic SignalProcessing ?

In this paper we demonstrate the application of the Frobenius-Perron operator to the statistical analysis of chaotic systems. The Frobenius-Perron operator is the main analysis tool whenever statistical properties of the generated and processed signals are of interest. One important eld of application are systems, where information is located in a particular statistic of the chaotic signal. For...