Inverse limits of certain interval mappings as attractors in two dimensions. (English) Zbl 0708.58012

From author’s abstract: “Let p be a continuous piecewise monotonic transitive map of the unit interval into itself such that, for positive iterations, the orbit of every critical point is finite and does not contain critical points. It is proved that for each two-dimensional manifold M, the inverse limit map of p is conjugate to an attractor of some \(C^ 1\)-diffeomorphism of M into itself, which is of class \(C^{\infty}\) outside some finite invariant set and can be chosen from an arbitrary diffeotopy class.”
Reviewer: A.Stone


37B99 Topological dynamics
37E99 Low-dimensional dynamical systems
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
Full Text: DOI EuDML