Homoclinic tangencies near cascades of period doubling bifurcations
This interesting paper shows that Feigenbaum maps in \(\mathbb R^n\) (maps that are accumulated by period doubling bifurcations) are approximable, in the \(C^r\) topology for \(r\) large enough, by maps with homoclinic tangencies. To obtain this result, the authors generalize the renormalization theory of \textit{A. M. Davie} [Commun. Math. Phys. 176, No. 2, 261-272 (1996; Zbl 0906.58012)] for \(C^{2 + \varepsilon}\) unimodal maps on the interval, to a renormalization theory in \(\mathbb R^n\) for \(C^r\) maps with \(r\) large enough.
scientific article; zbMATH DE number 1172082
scientific article