MSC2010 05C62, 14J80, 37D15
On the dynamics of bifurcation diffeomorphisms of a simple arc
E. V. Nozdrinova1, O. V. Pochinka2
| Annotation | 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. |
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| Keywords | bifurcation 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
