Invariant measures for singular hyperbolic attractors

E. A. Sataev

Sbornik. Mathematics, Tome 201 (2010) no. 3, pp. 419-470

Résumé

This paper continues the author's previous paper, where strong unstable spaces were constructed for a singular hyperbolic attractor. In this paper the existence of local strongly unstable manifolds and invariant measures of Sinaǐ-Bowen-Ruelle type is established. The properties of such measures are studied. It is proved that the number of ergodic components is finite and the set of periodic trajectories is dense. Bibliography: 34 titles.

Détail

Keywords: singular hyperbolic systems, unstable manifolds, invariant measures, ergodicity.

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