Inhomogeneities in chainable continua
Abstract
We study a class of chainable continua which contains, among others, 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 nonhyperbolic 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 side product we also obtain a characterization of arcs as inverse limits for piecewise monotone bonding maps, which is interesting in its own right.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 DOI:
 10.48550/arXiv.2002.07286
 arXiv:
 arXiv:2002.07286
 Bibcode:
 2020arXiv200207286A
 Keywords:

 Mathematics  Dynamical Systems
 EPrint:
 Appendix A is written by Henk Bruin. 28 pages, 11 figures