부산대학교 도서관

We consider three-dimensional diffeomorphisms having simultaneously heterodimensional cycles and heterodimensional tangencies associated to saddle-foci. These cycles lead to a completely nondominated bifurcation setting. For every r{\geqslant } 2, we exhibit a class of such diffeomorphisms whose heterodimensional cycles can be C^r stabilised and (simultaneously) approximated by diffeomorphisms with C^r robust homoclinic tangencies. The complexity of our nondominated setting with plenty of homoclinic and heteroclinic intersections is used to overcome the difficulty of performing C^r perturbations, r\geqslant 2, which are remarkably more difficult than C^1 ones. Our proof is reminiscent of the Palis-Takens' approach to get surface diffeomorphisms with infinitely many sinks (Newhouse phenomenon) in the unfolding of homoclinic tangencies of surface diffeomorphisms. This proof involves a scheme of renormalisation along nontransverse heteroclinic orbits converging to a center-unstable Hénon-like family displaying blender-horseshoes. A crucial step is the analysis of the embeddings of these blender-horseshoes in a nondominated context. [ABSTRACT FROM AUTHOR]