Abstract. In this note we show that a diffeomorphism which has a Hopf's bifurcation point, can be C 2 perturbed around the bifurcation point in order to get a diffeomorphism which exhibits homoclinic tangencies. In the C 3 case this is not possible because of the typical unfolding of a Hopf's bifurcation point.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.