Period-doubling bifurcation in a simple arc connecting Pixton's diffeomorphisms
O. V. Pochinka1, A. A. Romanov2
| Annotation | Pixton's diffeomorphism determined that it is structurally stable and its nonwandering set consists of exactly four points: two sinks, a source and a saddle. Class of such diffeomorphisms include representatives with the wild behavior of the separatrices. However, as in \cite{BoGrMePo07} was proved that all Pixton's diffeomorphisms whose nonwandering set consists of fixed points are connected by a simple arc. In this arc only saddle-node bifurcation exists. In this paper we construct a simple arc with period-doubling bifurcation between Pixton's diffeomorphism with periodic sinks and diffeomorphism of ``source-sink''. Using the results and \cite{BoGrMePo07}, it is possible to claim that a simple arc between any Pixton's diffeomorphisms exist |
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| Keywords | Pixton's diffeomorphism, simple arc, period-doubling bifurcation. |
1Docent of theory function chair of Nizhny Novgorod State University after N.I. Lobachevsky; olga-pochinka@yandex.ru
2Undergraduate of theory function chair of Nizhny Novgorod State University after N.I. Lobachevsky; romanov18.04@mail.ru
Citation: O. V. Pochinka, A. A. Romanov, "[Period-doubling bifurcation in a simple arc connecting Pixton's diffeomorphisms ]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,14:3 (2012) 74–79 (In Russian)
