On a structure of the space wandering orbits of diffeomorphisms on surfaces with the finite hyperbolic chain recurrent set
T.M. Mitryakova1, O. V. Pochinka2, A. E. Shishenkova3
| Annotation | In the present paper a class $\Phi$ of diffeomorphisms on surfaces $M^2$ with the finite hyperbolic chain recurrent set is considered. To each periodic orbit $\mathcal O_i, i=1,\dots,k_f$ of $f\in\Phi$ corresponds a representation of the dynamics of a diffeomorphism $f$ in the form ``source --- sink'', where source (sink) is a repeller $R_i$ (an attractor $A_i$) of diffeomorphism $f$. It is assigned that the orbit space of the wandering set $V_i=M^2\setminus(A_i\cup R_i)$ is a collection of the finite number of two-dimention torus. It implies, in particular, that the restriction of $f$ to $V_i$ is topologically conjugated with the homothety. |
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| Keywords | chain recurrent set, space of orbits, attractor, repeller. |
1Assistant of Theory Function Chair, Nizhny Novgorod State University after N.I. Lobachevsky, Nizhny Novgorod; tatiana.mitryakova@yandex.ru.
2Associate Professor of Theory Function Chair, Nizhny Novgorod State University after N.I. Lobachevsky, Nizhny Novgorod; olga-pochinka@yandex.ru.
3Associate Professor of Higher Mathematics, Nizhny Novgorod State Agricultural Academy, Nizhny Novgorod; math@agri.sci-nnov.ru.
Citation: T.M. Mitryakova, O. V. Pochinka, A. E. Shishenkova, "[On a structure of the space wandering orbits of diffeomorphisms on surfaces with the finite hyperbolic chain recurrent set]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,13:1 (2011) 63–70 (In Russian)
