Geodesic
Shadowing and expansivity in subspaces
Andrew D. Barwell 1   ; Chris Good 2   ; Piotr Oprocha 3
1 Heilbronn Institute for Mathematical Research University of Bristol Howard House, Queens Avenue Bristol, BS8 1SN, UK
2 School of Mathematics University of Birmingham Birmingham, B15 2TT, UK
3 Faculty 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
Fundamenta Mathematicae, Tome 219 (2012) no. 3, pp. 223-243 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm219-3-2
Keywords: address various notions shadowing expansivity continuous maps restricted proper subset their domain prove equivalences shadowing expansive properties demonstrate under what conditions certain expanding maps have shadowing generalize known results area investigate impact theory maps interval

Andrew D. Barwell  1   ; Chris Good  2   ; Piotr Oprocha  3

1 Heilbronn Institute for Mathematical Research University of Bristol Howard House, Queens Avenue Bristol, BS8 1SN, UK
2 School of Mathematics University of Birmingham Birmingham, B15 2TT, UK
3 Faculty 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 
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Andrew D. Barwell; Chris Good; Piotr Oprocha. Shadowing and expansivity in subspaces. Fundamenta Mathematicae, Tome 219 (2012) no. 3, pp. 223-243. doi: 10.4064/fm219-3-2

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