Inhomogeneities in chainable continua
Volume 254 / 2021
Fundamenta Mathematicae 254 (2021), 69-98
MSC: Primary 37B45; Secondary 37E05, 37E10, 37E30.
DOI: 10.4064/fm907-8-2020
Published online: 25 January 2021
Abstract
We study a class of chainable continua which contains all inverse limit spaces generated by a single interval bonding map which is piecewise monotone and locally eventually onto. Such spaces are realized as attractors of non-hyperbolic surface homeomorphisms. Using dynamical properties of the bonding map, we give conditions for existence of endpoints, characterize the set of local inhomogeneities, and determine when it consists only of endpoints. As a by-product we also obtain a characterization of arcs as inverse limits for piecewise monotone bonding maps, which is interesting in its own right.
