Decay in norm of transfer operators for semiflows

TL;DR

This paper proves that transfer operators for certain semiflows exhibit exponential decay in the H"older norm, leading to rapid mixing properties for these dynamical systems.

Contribution

It establishes exponential decay rates of transfer operators in H"older norms for both uniform and nonuniform semiflows, advancing understanding of their statistical properties.

Findings

Exponential decay of transfer operators in H"older norm.

Rapid mixing for uniformly and nonuniformly expanding semiflows.

Improved understanding of decay of correlations in dynamical systems.

Abstract

We establish exponential decay in H\"older norm of transfer operators applied to smooth observables of uniformly and nonuniformly expanding semiflows with exponential decay of correlations.