In this note we give a computable criterion for a piecewise expanding interval map T to be mixing, which at the same time not only establishes explicit bounds on the spectral gap of the associated Perron Frobenius operator acting on the space of functions of bounded variation, but establishes strict contraction rates for this operator. Of course such a result cannot be completely general, but o...

This manuscript introduces a regression-type formulation for approximating the Perron-Frobenius Operator by relying on distributional snapshots of data. These may represent densities particles. The Wasserstein metric is leveraged to define suitable functional optimization in space distributions. allows seeking dynamics so as interpolate flow function space. A first-order necessary condition opt...

We propose a notion of Frobenius-Perron dimension for certain free Z \mathbb {Z} </mml:semant...

We describe a fast and accurate method to compute the pressure and equilibrium states for maps of the interval T:[0,1]-->[0,1] with respect to potentials phi:[0,1]-->R. An approximate Ruelle-Perron-Frobenius operator is constructed and the pressure read off as the logarithm of the leading eigenvalue of this operator. By setting phi identical with 0, we recover the topological entropy. The confo...

In this paper, we study random Blaschke products, acting on the unit circle, and consider cocycle of Perron–Frobenius operators Banach spaces analytic functions an annulus. We completely describe Lyapunov spectrum these cocycles. As a corollary, obtain simple product system where has infinitely many distinct exponents, but arbitrarily small natural perturbations cause complete collapse spectrum...

We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator that generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the c...