An entropy dichotomy for singular star flows
Abstract
We show that non-trivial chain recurrent classes for generic C1 star flows satisfy a dichotomy: either they have zero topological entropy, or they must be isolated. Moreover, chain recurrent classes for generic star flows with zero entropy must be sectional hyperbolic, and cannot be detected by any non-trivial ergodic invariant probability. As a result, we show that C1 generic star flows have only finitely many Lyapunov stable chain recurrent classes.
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