TY - JOUR

T1 - Mixing for suspension flows over skew-translations and time-changes of quasi-abelian filiform nilflows

AU - Ravotti, Davide

PY - 2019/12

Y1 - 2019/12

N2 - We consider suspension flows over uniquely ergodic skew-translations on a (Formula presented.)-dimensional torus (Formula presented.) for (Formula presented.). We prove that there exists a set (Formula presented.) of smooth functions, which is dense in the space (Formula presented.) of continuous functions, such that every roof function in (Formula presented.) which is not cohomologous to a constant induces a mixing suspension flow. We also construct a dense set of mixing examples which is explicitly described in terms of their Fourier coefficients. In the language of nilflows on nilmanifolds, our result implies that, for every uniquely ergodic nilflow on a quasi-abelian filiform nilmanifold, there exists a dense subspace of smooth time-changes in which mixing occurs if and only if the time-change is not cohomologous to a constant. This generalizes a theorem by Avila, Forni and Ulcigrai [Mixing for time-changes of Heisenberg nilflows.

AB - We consider suspension flows over uniquely ergodic skew-translations on a (Formula presented.)-dimensional torus (Formula presented.) for (Formula presented.). We prove that there exists a set (Formula presented.) of smooth functions, which is dense in the space (Formula presented.) of continuous functions, such that every roof function in (Formula presented.) which is not cohomologous to a constant induces a mixing suspension flow. We also construct a dense set of mixing examples which is explicitly described in terms of their Fourier coefficients. In the language of nilflows on nilmanifolds, our result implies that, for every uniquely ergodic nilflow on a quasi-abelian filiform nilmanifold, there exists a dense subspace of smooth time-changes in which mixing occurs if and only if the time-change is not cohomologous to a constant. This generalizes a theorem by Avila, Forni and Ulcigrai [Mixing for time-changes of Heisenberg nilflows.

UR - http://www.scopus.com/inward/record.url?scp=85044460874&partnerID=8YFLogxK

U2 - 10.1017/etds.2018.19

DO - 10.1017/etds.2018.19

M3 - Article

AN - SCOPUS:85044460874

VL - 39

SP - 3407

EP - 3436

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 12

ER -