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In this note we show that a diffeomorphism which has a Hopf’s bifurcation point, can be C2 perturbed around the bifurcation point in order to get a diffeomorphism which exhibits homoclinic tangencies. In the C3 case this is not possible because of the typical unfolding of a Hopf’s bifurcation point.

𝐶²-perturbations of Hopf’s bifurcation points and homoclinic tangencies