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

Abstract

For high dimensional transformations, the essential spectral radius of the Perron–Frobenius operator restricted to some natural space is generally smaller than the reciprocals of the radius of convergence of the dynamical zeta function. We will construct transformations whose essential spectral radius coincide with the reciprocal of the radius of convergence of the dynamical zeta functions, and construct new type of 2 dimensional low discrepancy sequences.