### The example of a diffeomorfism <<source-sink>> which does not include to a smooth flow

#### O. V. Pochinka1, A. A. Romanov2

Annotation The inclusion to a topological flow of any two-dimensional gradient-like cascade with condition that all its non-wandering points are fixed is one of the classical results of J.Palis \cite{Pa}. In contrast, a nowhere dense set of them are included in a smooth flow, it follows from the \cite{Brin}. The analytic construction of an example of the diffeomorfism <> on $\mathbb {S}^2$ which does not include to a smooth flow is the purpose of this paper. diffeomorfism <>, inclusion to a smooth flow

1Professor of theory function chair, Nizhny Novgorod State University after N.I. Lobachevsky; olga-pochinka@yandex.ru

2Undergraduate of theory function chair, Nizhny Novgorod State University after N.I. Lobachevsky; romanov18.04@mail.ru

Citation: O. V. Pochinka, A. A. Romanov, "[The example of a diffeomorfism <> which does not include to a smooth flow]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,15:3 (2013) 123–125 (In Russian)