Smooth mixing flows with purely singular spectra. (English) Zbl 1099.37018

Fayad, Bassam

Duke Math. J. 132, No. 2, 371-391 (2006).

Summary: We give a geometric criterion that implies a singular maximal spectral type for a dynamical system on a Riemannian manifold. The criterion, which is based on the existence of fairly rich but localized periodic approximations, is compatible with mixing. Indeed, we check it for an ad hoc class of smooth mixing flows on \(\mathbb{T}^3\) obtained from linear flows by time change and thus providing natural examples of mixing smooth diffeomorphisms and flows with purely singular spectra.

MSC:

37C40	Smooth ergodic theory, invariant measures for smooth dynamical systems
37A25	Ergodicity, mixing, rates of mixing

Keywords:

singular maximal spectral type; periodic approximations; mixing; smooth diffeomorphisms and flows

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