Mixing and eigenfunctions of singular hyperbolic attractors

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.
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