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MSC2010 05C62, 14J80, 37D15

On the dynamics of bifurcation diffeomorphisms of a simple arc

E. V. Nozdrinova1, O. V. Pochinka2

AnnotationIn 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.
Keywordsbifurcation points, simple arc.

1Elena V. Nozdrinova, Trainee Researcher, Laboratory of Topological Methods in Dynamics, National Research University <<Higher School of Economics>> (25/12, Bolshaya Pecherskaya st., 603155 Nizhny Novgorod, Russia), ORCID: http://orcid.org/0000-0001-5209-377X, maati@mail.ru

2Olga V. Pochinka, Laboratory Head, Laboratory of Topological Methods in Dynamics, National Research University <<Higher School of Economics>> (25/12, Bolshaya Pecherskaya st., 603155 Nizhny Novgorod, Russia), ORCID: http://orcid.org/0000-0002-6587-5305, olga-pochinka@yandex.ru

Citation: E. V. Nozdrinova, O. V. Pochinka, "[On the dynamics of bifurcation diffeomorphisms of a simple arc]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,20:1 (2018) 30–38 (In Russian)

DOI 10.15507/2079-6900.20.201801.30-38