Star flows are considered as “most” hyperbolic systems when the systems exhibit singularities. For hyperbolic systems, Sinai, Rulle and Bowen showed that there exists finitely many physical measures and their basins have full Lebesgue-measure. Palis conjectured that most systems should exhibit finitely many physical measures and their basin cover the whole manifold in the sense of Lebesgue measure. In this talk, we will discuss the Palis conjecture for star flows. This is based on a joint work with S. Crovisier, X. Wang and D. Yang.

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