Shadowing and expansivity in subspaces

Volume 219 / 2012

Andrew D. Barwell, Chris Good, Piotr Oprocha Fundamenta Mathematicae 219 (2012), 223-243 MSC: 37B45, 37E05, 54F15, 54H20. DOI: 10.4064/fm219-3-2

Abstract

We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.

Authors

  • Andrew D. BarwellHeilbronn Institute for Mathematical Research
    University of Bristol
    Howard House, Queens Avenue
    Bristol, BS8 1SN, UK
    e-mail
  • Chris GoodSchool of Mathematics
    University of Birmingham
    Birmingham, B15 2TT, UK
    e-mail
  • Piotr OprochaFaculty of Applied Mathematics
    AGH University
    of Science and Technology
    Mickiewicza 30
    30-059 Kraków, Poland
    and
    Institute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    e-mail

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