Destroyable restrictive intervals and two unimodal map models arbitrarily close to homoclinic tangencies (Q2784732)

By definition for an interval map \(f\), a restrictive interval \({\mathfrak M}\) may be thought of as a renormalization domain where \(f^n: {\mathfrak M}\to {\mathfrak M}\) for some \(n\geq 1\). Here the author shows that for a class of unimodal maps there are only three ways for a map to have a destroyable restrictive interval. Moreover, he discusses two qualitatively different unimodal map models with destroyable restrictive intervals and shows that if \(f\) is either of these map models, then \(f\) itself does not necessarily have a homoclinic tangency, but there is a unimodal map \(g\) arbitrarily close to \(f\) with a homoclinic tangency.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00016].