Higher dimensional topology and generalized Hopf bifurcations for discrete dynamical systems

Abstract

<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 result allows us to obtain sharper Hopf bifurcation theorems for fixed points in the general case and other attractors in low dimensional manifolds. Topological techniques based on the notion of concentricity of manifolds play a substantial role in the paper.</p>