On the creation of homoclinic points (Q1118879)

The paper deals with \(C^ r\)-diffeomorphisms of a manifold to itself having almost homoclinic points corresponding to some hyperbolic fixed point p. The problem considered is the existence of arbitrarily close \(C^ r\)-diffeomorphisms having homoclinic points. For \(r=1\) or 2 this is proved under an additional assumption involving certain probability measures on the manifold. The proof is actually given for a stronger result in the case of hyperbolic sets.