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Inhomogeneities in chainable continua

Volume 254 / 2021

Ana Anušić, Jernej Činč, Henk Bruin 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.

Authors

  • Ana AnušićDepartamento de Matemática Aplicada
    IME-USP, Rua de Matão 1010
    Cidade Universitária
    05508-090 São Paulo SP, Brazil
    e-mail
  • Jernej ČinčAGH University of Science and Technology
    Faculty of Applied Mathematics
    Mickiewicza 30
    30-059 Kraków, Poland
    and
    National Supercomputing Centre IT4Innovations
    Division of the University of Ostrava
    Institute for Research and Applications of Fuzzy Modeling
    30. Dubna 22
    70103 Ostrava, Czech Republic
    e-mail
  • Henk BruinFaculty of Mathematics
    University of Vienna
    Oskar-Morgenstern-Platz 1
    A-1090 Wien, Austria
    e-mail

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