On physical measures of star vector fields
Jinhua Zhang (Beihang University)

Sinai, Ruelle and Bowen studied the ergodic properties of uniform hyperbolic systems and showed that such systems have finitely many physical measures whose union has full Lebesgue measure. For dynamics beyond uniform hyperbolicity, existence and finiteness of physical measures are widely open. Star vector fields, including the famous Lorenz attractor, is beyond uniform hyperbolicity and play an important role in the study of stability conjectures. In this talk, we will show the existence and finiteness of physical measures for typical star vector fields. This talk is based on a joint work with S. Crovisier, X. Wang and D.Yang.