Lyapunov stable chain recurrence classes for singular flows
Abstract
We show that for a C1 generic vector field X away from homoclinic tangencies, a nontrivial Lyapunov stable chain recurrence class is a homoclinic class. The proof uses an argument with C2 vector fields approaching X in C1 topology, with their Gibbs F-states converging to a Gibbs F-state of X.
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