For any C1 perturbation of a vector field with a sectional hyperbolic set, the number of homoclinic classes inside a fixed neighborhood is uniformly bounded.
The global dynamics of C 1-generic diffeomorphisms or flows
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Finiteness of homoclinic classes on sectional hyperbolic sets
For any C1 perturbation of a vector field with a sectional hyperbolic set, the number of homoclinic classes inside a fixed neighborhood is uniformly bounded.