Period-doubling bifurcation in a simple arc connecting Pixton's diffeomorphisms

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 [2] 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 [2], it is possible to claim that a simple arc between any Pixton's diffeomorphisms exist.