Generation of homoclinic tangencies by $C^1$-perturbations
Generation of homoclinic tangencies by $C^1$-perturbations
Given a $C^1$-diffeomorphism $f$ of a compact manifold, we show that if the stable/unstable dominated splitting along a saddle is weak enough, then there is a small $C^1$-perturbation that preserves the orbit of the saddle and that generates a homoclinic tangency related to it. Moreover, we show that the perturbation …