Bifurcations under Nondegenerated Conditions of Higher Degree and a New Simple Proof of the Hopf]Neimark]Sacker Bifurcation Theorem

This paper generalizes the nondegenerated conditions that imply the most common bifurcations in uniparametric families of maps defined on R. It also presents a new very simple proof of the Hopf bifurcation theorem of maps on R2 see G. Iooss, ‘‘Mathematical Studies,’’ Vol. 36, 1979.., based on one of the results obtained in one dimension and generalizes one of the nondegenerated conditions the Hopf condition.of the theorem