Correction to "Cutting surfaces and applications to periodic points and chaotic-like dynamics"

Abstract

After the publication of the article, we have noticed that in Lemma 5.11 the hypothesis of injectivity for the map $\psi$ is missing. Hence the lemma has to be corrected by adding the assumption ``$\psi$ is injective on ${\mathcal D}$.'' With this modification we also obtain that $\psi(\Lambda) = \Lambda$ and the proof can be simplified. Without the injectivity assumption, it holds that $\psi|_{\Lambda}$ is semicongiugate to the one-sided $m$-shift (and not to the two-sided as stated). In our applications to ODEs, the function $\psi$ is the Poincaré map (a homeomorphism) and therefore this change doesn't affect the meaningfulness for differential systems. We point out that Lemma 5.11 is considered only with the aim of giving an interpretation about the chaotic dynamics found with our approach. For all the other results, we don't need any injectivity assumption on the maps which are involved.