One sided branching in Anosov foliations
Let \({\mathcal F}^s\) and \({\mathcal F}^u\) be the stable and unstable 2-dimensional (Anosov) foliations of the Anosov flow \(\Phi\) on \(M^3\) and \(\widetilde{\mathcal F}^s\), \(\widetilde{\mathcal F}^u\) the respective lifts to the universal cover. Their leaf spaces are 1-dimensional manifolds, if they are Hausdorff then they are homeomorphic to the real line \(\mathcal R\), otherwise we say that the foliation has branching. We say that \(\widetilde{\mathcal F}^s\) (or \(\widetilde{\mathcal F}^u\)) has one sided branching if its leaf space is not \(\mathcal R\) but the branching occurs only in the positive (or negative) transversal direction. Main theorem: Let \(\Phi\) be a topological transitive Anosov flow in \(M^3\). If one of \(\widetilde{\mathcal F}^s\) or \(\widetilde{\mathcal F}^u\) has branching then both \(\widetilde{\mathcal F}^s\) or \(\widetilde{\mathcal F}^u\) have branching in the positive and negative directions.
scientific article; zbMATH DE number 790581