Invariant measures for singular hyperbolic attractors. (English. Russian original) Zbl 1203.37045

Sataev, E. A.

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.

Reviewer: Anke Pohl (Zürich)

MSC:

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

Keywords:

singular hyperbolic systems; unstable manifolds; invariant measures; ergodicity