Abundance of $C^1$-robust homoclinic tangencies

C. Bonatti, L. J. Diaz

A diffeomorphism $f$ has a $C^1$-robust homoclinic tangency if there is a $C^1$-neighbourhood $\cU$ of $f$ such that every diffeomorphism in $g\in \cU$ has a hyperbolic set $\La_g$…