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Invariant measures for singular hyperbolic attractors. (English. Russian original) Zbl 1203.37045
Sb. Math. 201, No. 3, 419-470 (2010); translation from Mat. Sb. 201, No. 3, 107-160 (2010).
For a singular hyperbolic flow the existence of local strong unstable manifolds and invariant measures of Sinaĭ-Bowen-Ruelle measures is shown. Moreover, it is proved that these measures have only finitely many ergodic components and that the set of periodic trajectories is dense in each ergodic component.

MSC:
37D10 Invariant manifold theory for dynamical systems
37D30 Partially hyperbolic systems and dominated splittings
34D45 Attractors of solutions to ordinary differential equations
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