Higher dimensional topology and generalized Hopf bifurcations for discrete dynamical systems

<p style='text-indent:20px;'>In this paper we study generalized Poincaré-Andronov-Hopf bifurcations of discrete dynamical systems. We prove a general result for attractors in <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula>-dimensional manifolds satisfying some suitable conditions. This allows us to obtain sharper Hopf bifurcation theorems fixed points the case and other low dimensional manifolds. Topological techniques based on notion concentricity play substantial role paper.</p>