On the dynamics of bifurcation diffeomorphisms of a simple arc

In this paper we consider the class of diffeomorphisms of a closed $n$-dimensional manifold that are bifurcation points of simple arcs in the space of diffeomorphisms. The concept of a simple arc arose as a result of research by S. Newhouse, J. Palis and Fl. Takens. They showed that a generic set of arcs starting in a Morse-Smale system have a diffeomorphism with a regular dynamics as the first bifurcation point. Namely, the non-wandering set of such a diffeomorphism is finite, but unlike Morse-Smale systems, it can have either one non-hyperbolic periodic orbit that is a saddle-node or a flip, or one orbit of a non-transversal intersection of invariant manifolds of periodic points. The authors studied the asymptotic properties and the embedding structure of the invariant manifolds of non-wandering points of bifurcation diffeomorphisms of a simple arc. The possibility of complete ordering of periodic orbits of such diffeomorphisms is also established.