Geodesic
Mixing and eigenfunctions of singular hyperbolic attractors
Sbornik. Mathematics, Tome 206 (2015) no. 4, pp. 572-599

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This paper is concerned with investigating singular hyperbolic flows. It is shown that an eigenfunction cannot be continuous on an ergodic component containing a fixed point. However, it is continuous on a certain set (after a modification on a nullset). The following alternative is established: either there exists an eigenfunction on an ergodic component or the flow is mixing on this component. Sufficient conditions for mixing are given. Bibliography: 28 titles.
Keywords: singular hyperbolic attractor, invariant measure, mixing, eigenfunction. 
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     title = {Mixing and eigenfunctions of singular hyperbolic attractors},
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E. A. Sataev. Mixing and eigenfunctions of singular hyperbolic attractors. Sbornik. Mathematics, Tome 206 (2015) no. 4, pp. 572-599. http://geodesic.mathdoc.fr/item/SM_2015_206_4_a4/