Multiple mixing from weak hyperbolicity by the Hopf argument

Yves Coudène (1) , Boris Hasselblatt (2) , Serge Troubetzkoy (3, 4)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
2 Department of Mathematics
3 I2M - Institut de Mathématiques de Marseille
4 CPT - Centre de Physique Théorique - UMR 6207

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.

Mots clés: Anosov systems; mixing; multiple mixing; Hopf argument; ergodicity; hyperbolicity}

Domaines: Systèmes dynamiques [math.DS]

Yves Coudène, Boris Hasselblatt, Serge Troubetzkoy. Multiple mixing from weak hyperbolicity by the Hopf argument. 2014. ⟨hal-01006451v2⟩