Multiple mixing from weak hyperbolicity by the Hopf argument

TL;DR

This paper demonstrates that the Hopf argument can establish multiple mixing under weak hyperbolicity conditions, broadening the scope of classical results with simpler proofs and minimal assumptions.

Contribution

It introduces a novel approach showing that multiple mixing can be achieved with weak hyperbolicity, without requiring smoothness or exponential rates, thus extending classical hyperbolic theory.

Findings

Proves multiple mixing using weak hyperbolicity and the Hopf argument

Simplifies the proof of classical results in hyperbolic dynamics

Shows 'mixing implies multiple mixing' beyond classical hyperbolic systems

Abstract

We show that using only weak hyperbolicity (no smoothness, compactness or exponential rates) the Hopf argument produces multiple mixing in an elementary way. While this recovers classical results with far simpler proofs, the point is the broader applicability implied by the weak hypotheses. Some of the results can also be viewed as establishing "mixing implies multiple mixing" outside the classical hyperbolic context.