Geodesic
On the dynamics of bifurcation diffeomorphisms of a simple arc
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 1, pp. 30-38

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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.
Mots-clés : bifurcation points, simple arc. 
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     title = {On the dynamics of bifurcation diffeomorphisms of a simple arc},
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E. Nozdrinova; O. V. Pochinka. On the dynamics of bifurcation diffeomorphisms of a simple arc. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 1, pp. 30-38. http://geodesic.mathdoc.fr/item/SVMO_2018_20_1_a2/